"A Moosehead Journal," November 1853 Putnam's Monthly. describes an all-male moose-hunting trip to Maine. However, at one point he mentions meeting a woman:

(p. 468) "Kineo rises 1750 feet above the sea, and 750 above the lake. The climb is very easy, with fine outlooks at every turn, over lake and forest. Near the top is a spring of water. Near the spring we met a Bloomer! It was the first chronic one I had ever seen. It struck me as a sensible costume for the occasion."

"The Catskills" by T. Addison Richards, July 1854 Harper's Monthly

On  p. 157, the author describes being part of a mixed party of men and women hiking six miles, setting up camp, staying overnight and returning the next day. It includes this:

(p. 157) "Preceded by our guides, laden with stores, we made a very gallant appearance, not lessened by the orthodox costume of both ladies and gentlemen--the former in a demi-composite Bloomer rig. Through bush and brake, wading in deep mosses and clambering over and under fearful rocks, we merrily urged our way; now and then halting for a general council of travel, by the side of the cool mountain springs. The ladies performed the journey stoutly, until, without let or hindrance from bears, snakes, or panthers, we rested on the crown of the noble peak."

Going to Mount Katahdin," published in the September 1856 Putnam's Monthly, describes in detail a group of men and women camping and hiking up Mount Katahdin.

November/December 1859 Godey's, "Picnicking in the Pine Wood; or Fishing and Flirting at Thunder
Bay,” is online only through the subscription service Accessible Archives. A brief example:

"An excursion! Oh, that is delightful! Shall it be a boat-ride to the island, and a picnic beneath the old apple-tree, planted there by the French a hundred years ago? or a carriage ride to the fort? or what?"

"Oh, a much more serious affair!" replied Mr. Florence. "I have just been thinking of it, and have not yet spoken of it even to Lissa here. I warn you that but few of you will be pleased with the idea; only those who have plenty of courage, health, and a spice of adventure in their composition, will accept the proposition. You know I had to go up to Thunder Bay, last autumn, and wander around in that wild region for three weeks, with no company except that of my two men. I was desperately lonely; but I should have enjoyed it with good company. Why can't a party of you ladies propose yourselves for a regular camping-out frolic, and go along with me next time? I will promise to arm and equip the volunteers, and to find two or three gallant men to act as sentinels and aids-de-camp."

"The Adirondack; or, Life in the Woods," by J. T. Headley, 1869. The author describes meeting a group of women.

(page 311) "As they drew near, I discovered that two of the boats contained ladies. It was raining steadily, and they were apparently taking a cold bath. When the boats reaached shore, I saw, however, that they were well protected with gentlemen's India-rubber overcoats and rubber boots; so that, in a few minutes after they came out of their chrysalis state, they stood in their short dresses and Turkish trowsers as dry as though they had just emerged from their own apartments. They were the party of Judge E--- of Vermont, and had been up as far as Long Lake, at the foot of which they had encamped. The ladies, instead of grumbling at the mosquitoes and flies that had tormented them, and the cold rain through which they had been so long rowing, expressed great regret that they were compelled to leave the woods. These lakes, dotted with islands--the dark, solemn rivers running all day long, almost without a sound, through the still forest--the distant mountain views--the wildness and beauty that perpetually surround them, have a greater charm for the ladies than even the fine sporting has for gentlemen."

(Page 418-420)"As we passed down the lake, I saw on an open wooded point ahead, scarlet dresses and a mixed group that looked like a pic-nic party. As we came opposite they stepped into their boats and swept out into the lake. They had seen a shower rising over the forest, and were hastening to their camp. As they joined us, we discovered that they were our two acquaintances that we had left at Martin's with Judge ----- of Vermont and his family, who had come out to spend a few weeks in the woods. They invited us down to their camp to spend the night. We gladly accepted the invitation, and moved off together, six boats abreast, down the lake. Soon the rain began to come down in torrents, but the ladies were safely encased in oiled-silk capes and India rubber blankets, and laughed at the storm....

"The camp was pitched in a beautiful grove in a sheltered nook, and consisted of three tents--one for the guides, one for the gentlemen, and one for the ladies--the latter strewed with hemlock boughs and spread with buffalo robes. A table made of poles, resting on crotched sticks and covered with bark, stood in front, on which the guides soon had a smoking supper, composed of venison and trout."

Beginning on page 441 is a chapter on "Advice to ladies visiting the Adirondacks.” A brief quote:

(page 444) "Two classes of ladies now visit the Adirondack... in my recent and last visit I had six ladies under my charge, who were equally divided into these two classes. One class goes to the woods to rough it like any man. They like the tent-life--the distant exploration and the hunter's fare, and sometimes use his rifle or the sportsman's rod. To such I have nothing to say. Willing to take the evil and good together, the wild scenery and wilder life have a charm for them that makes them laugh at mosquitoes and the thousand little inconveniences to which they are subjected.

"But there is another large class who have no taste for these things—they want to see a little of the wilderness without being deprived of their usual comforts. These stay on the outskirts, while the others, with the gentlemen, press into the interior with their tents. Of course, Bloomer costume is alone fit for those who literally take to the woods. Now I found but very few of the great number that stayed in the outskirts who did not become disgusted, or at least discontented, and declared that they would never come again."

Information on day-trips:

"Virginia Illustrated, containing A Visit to the Virginia Canaan and Porte Crayon and His Cousins," published in 1871. It’s about a trip in the early 1850s, and was first published as a series in Harper's Monthly beginning in December of 1854

Rev. Henry Ward Beecher’s thoughts on women hiking, quoted below, are from “Star Papers: or Experiences of Art and Nature, 1855

(p. 155) "And, above all, let every woman have a bloomer dress, for the sake of
foot-excursions. In the city or town, our eye is yet in bondage to the old forms. But in the country, where the fields are to be traveled, the rocks climbed, brooks crossed and recrossed, fences scaled, bushes and weeds navigated, a woman in a long dress and multitudinous petticoats is a
ridiculous or a pitiable object. Something is always catching; the party is detained till each woman can gather up her flowing robes, and clutch them in her left hand, while a shawl, parasol and bonnet-strings fill up the right hand. Thus she is engineered over and around the rocks or logs; and, in spite of all pains and gallantry, returns home bedrabbled and ragged. A bloomer costume leaves the motion free, dispenses with half the help from without, and avoids needless exposure of one's person. If, ignorant of what is best, a fair friend is caught in the country without such suitable dress,
she is to be pitied, not blamed. But where one may have them, and rejects them for field-excursions as unbecoming and ridiculous, let me assure such foolish persons that it is the only dress that is really decent. I should think less of one's judgment and delicacy who, after a fair trial of both
dresses, in an excursion requiring much field-walking, was not-heartily converted to the theory of Bloomerism and to its practice in the country."

At Home and Abroad: A Sketch-book of life, scenery, and men.  By Bayard Taylor.  Chapt. XVIII. The Mammoth Cave. May 1855.

(p. 180) "The next morning we made preparations for an early start, as we had a long day's journey before us.  Our party was increased to eleven by the addition of a bridal pair, a young Tennessean, and two silent Boston gentlemen.  We had two guides:  Stephen, whom I had specifically engaged, and Mat.  The ladies, with one exception, were attired in Bloomer costume, greatly to the merriment of the party, but much to their own convenience.  Dresses are kept at the hotel for the use of lady visitors, and I would advise all such to make use of them."

The Living Age dated Feb. 2, 1861, Vol. 68, Issue 870 published out of New York gives an account entitled "Mammoth Cave": (p. 284) "After poking about in the bowels of the earth for three or four hours, visitors to the cave arrive at Echo River, where they embark on a disgustingly muddy scow, or if the party is large enough, two or three wretched boats are brought into requisition.  The women are all dressed in fancifully colored bloomer dresses, and with the uplifted lanterns, present a strange and weird appearance as the boat is pushed from shore, and floats down into the black gloom..."

And from an 1867 account from The Living Age, (p. 42) "Our guide relates, to keep our courage up, the fearful experience of a lady, too modest to appear in a bloomer, who tried to go through with crinoline:  she got through at last, but the crinoline never did."

Period accounts of Ladies Camping