People kept them on ships for fresh eggs so it's certainly possible.
Starting with warmth,
chickens really don't need any unless you live somewhere really really cold they will do fine so long as they are out of the wind, and have a perch that lets them get their feathers down over their feet.
A frame runs/coops are pretty common so again perfectly possible.
Personaly I do not like chicken tractors or runs I built one myself which was 15ft long by 4ft wide with a suspended house and I found it cruel to keep them in such a small area but I am aware I am in a minority here.
If I were trying to do moveable chickens I would make a small house for them with a perch and a nesting box and a good lockable door. this would be their house when you are set up and their crate when you move. and then I would buy some electric poultry netting and a
solar charger, that way the chickens could get as much or as little space as wherever you stopped had, and it would take very little room when you were packed up and moving.
I have no idea how stressed/not stressed they would be but I expect they would soon get used to it.