They make a mess, lots of poop. So you will want them up off the ground or floor so you can clean up after them. You don't want them living in their own piles of poop. I recommend a cage. A 24 x 24 like a rabbit cage is big enough. YOu can still put it in your shed with a light on them for 16 hours and cover them at night. I keep a broom and shovel near the cages so I can clean up after mine after I do the food and water. You can get the rabbit cage that has a tray under it and just dump it out or put kitty litter in it or some other kind of litter to keep down the smell. Well you may not have much of a smell in the winter but it will make clean up easier.
We just moved ours in the shed today. We moved the grower pen and the layers in there too. We made a stand for the layers cage. They are in a double pen that is 3' x 3' square. I put a wall in the middle and a door for each side. Anyway, we cut a moving blanket to fit around the wire part of the grower pen and let it reach down to nearly the floor and nailed it so I can lift it on warmer days. There are spaces along where the top lays down for air flow and we have a heat lamp for one side but both sides will benefit from it. The youngert ones are in the side with the light and they have a little house under the light to get into for further heat. We put in a floreescent light directly over the layers so they can have light for their 16 hours a day. I just cover the cage at night so they can't get a draft. I can clean under the pens too.