It's actually a very interesting topic. Focusing on the late 18th century since you mentioned Turn, campaign furniture was something readily available to officers for purchase. According to the European model for military officers purchased their own tent, uniform, furniture, etc. They are only restricted by their own pocket book and the amount of space afforded to them on the baggage wagons. Since the purpose of campaigning was to be able to move quickly and easily, the furniture and tents must as well.

One of the easiest examples to look at is George Washington. He had two Marquees (large oval tents) that served as his headquarters. Most officers only had one, but his second served as a more public dining and meeting space. His personal marquee was 24'x14' and 10' high (at least the second one made over the winter of 1777/78 was and still survives) serving as office, bedroom, and storage. In terms of floor covering we don't know specifically what he had yet. He does purchase carpets, which could have been used on top of wood floors (think of the temporary dance floors used by DJs today). Painted floor cloths or even simply hay/straw could also be used. In terms of his furniture he had a bed which survives at Mount Vernon that folds up into the trunk you see just below it in the picture (it's about 14"x14"x40"). His mattress, pillows, and bedding packed into leather valises for travel. We know he purchased 18 camp stools and 3 camp tables that packed into three crates. He also had trunks to carry his paperwork and canteens to carry his dishware/utensils. A good deal of stuff to carry around, but he was not only responsible for himself, but his officers as well.

Campaign furniture comes in many designs, but the main purpose is to be easily transported and take up the smallest amount of room possible when packed. There's an entire book on British Campaign Furniture for further reading.