I would guess many people use a tent of some type. Others may sleep in their vehicle if it is large enough or has been specifically retrofitted for that. In Big Sky country, I suspect some sleep under the stars using a simple tarp and bivy.
For me, it has mostly been a backpacking tent which is designed to be minimalist, light, and small. It serves its purpose but affords very little luxury. I have several backpacking tents but currently am using a Six Moons Designs Lunar Duo. They call it roomy for one but I would beg to differ especially when I'm hauling extra gear that we all have specifically for sasquatching. In some areas I sasquatch in, there are lean-tos and I always use them as they provide shelter without having to carry a single additional ounce in your backpack.
When I can reach an area with a 4x4, I luxuriate in my Cabela's 8-man Alaskan Guide tent. Love that tent. It is the bomb. Roomy, I can stand up in it, and will withstand just about anything Mother Nature can throw at it.
https://www.youtube.com/watch?v=PylrnSDprIM
Just this week, I ordered a new tent that I'm hopeful will revolutionize my outdoor adventures. It is a 4-man tipi (versus a pyramid) from Seek Outside that allows the ability to "hot tent". It has a stove jack so I can carry a wood stove with me. It will very comfortably house two people, stove, wood, and all the gear you have. The total weight of tent and wood stove will be light enough to be backpacked alone but can be split with another person when a friend joins me. It's tall enough, at 6'10", to be able to stand up in it (PG - you'll need the 6-man tipi !!). Best of all, I can run the wood stove and dry clothes, boots, gear, and cook. On cooler or cold nights, I'll be able to sit in the tent in a teeshirt in 80F conditions rather than cocooned in down clothing and fleece in sub-freezing temperatures.
Pretty excited about this new tent. It is light enough to backpacked alone, will provide a ton of space (including head space) compared to what I am used to, and will allow more comfortable arrangements in colder months. In warm months, I'll ditch the Lunar Duo and backpack with this tent.
https://seekoutside.com/
What do you folks use for housing arrangements while out in the field?
p.s. This is the 8-man version of the tent as I didn't see any 4-man tipi videos I liked: