In the American Civil War soldiers generally carried very little, usually just a blanket and a shelter half. If there was any more elaborate sleep system, it was transported by wagon or pack train. If you read How to Camp Out by John M. Gould, 1877 you can get a good feel for the type of gear that was used right after the war, and what the common practices were. They generally didn't travel through the woods. Travel was on roads, and they stayed in camps or towns.
The traditional method for insulating in cold weather was furs.
"The Bed of a mountaineer is an article neither complex in its nature nor difficult in its adjustment. A single buffalo robe folded double and spread upon the ground, with a rock, or knoll, or some like substitute for a pillow, furnishes the sole base-work upon which the sleeper reclines, and, enveloped in an additional blanket or robe, contentedly enjoys his rest." Rufus Sage, Rocky Mountain Life, or Startling Scenes and Perilous Adventures in the Far West, During an Expedition of Three Years, 1846
"We spread our apischimos on the ground out on the open prairie and covered ourselves with riding cloaks and buffalo robes.... We called to our dogs to lie on top of us, as usual, for the purposes of keeping guard and also of imparting warmth. But those canines were every instant scenting nearby wolves, bounding off with great outcry to fight the beasts or drive them away, then lying down on top of us again, scratching themselves and contesting one another's places. Under such restless, disquieting conditions, especially in our overexcited state, we were unable to sleep at all." Rudolph Freiderich Kurtz, The Journal of Rudolph Friederich Kurz, 1846
"We awoke on the morning of the 16th with a Norther penetrating our blankets. The river Arkansas, almost dry, and on whose north bank we were encamped, was covered with floating particles of thin ice. Drinker had but two blankets, and on awakening we found him lying near the remains of the bois de vache fire, the light ashes of which, on his clothing, gave the appearance of snow. We wore extra clothing during the mornings ride, and Drinker looked bad from the effects of last nights wakefulness. We rode in silence for a time, somewhat in advance of the party, in vain attempts to encourage conversation. At length, after a long pause, he said, St. Vrain and Folger sleep together; Chad and Bransford do too. Hadnt we better? I acquiesced with pleasure. With saddles and over coats, we had good pillows-the other clothing remained on us. Wherever camp was made, a place was selected by each couple for sleeping before dismounting (mountaineer custom); and, ere dark, the pallet of robes was always spread. We huddled around the miserable cow wood fires, chilled by the cold winds." Lewis Garrand, Wah-to-yah and the Taos Trail, 1850
Of course, such as sleep system was not carried in a pack. Travel was done either by boat or pack train.
In the late 19th and early 20th century the browse bag (a thin cotton bag filled with whatever was around) seemed to have been the preferred sleeping surface.