That looks more than adequate for 3 hens. I wouldn't bother making the roost/nest area any bigger. Keep them sheltered from wind and keep them dry and you'll be fine. My first tractor was much smaller than that and I did 3 hens one year (I did let them free range sometimes).
Be careful about expanding the run - you'll wind up wanting to add more birds!

The garden Ark is plenty big enough for 3 chickens. I would not change it. The purpose of a chicken tractor is that it is moveable, you would need to move it at least every two or three days. During the winter I would put the plywood over the top or a good tarp. This will keep rain, snow and drafts off the chickens. You need some ventilation during the winter to keep the air inside the coop fresh so the chickens won't get sick. Always place the tractor with the back to the wind you don't want it coming in thru the door.

Remember chickens are covered with feathers and they are well insulated. Plus they will keep each other warm as necessary. My chicken are in ventilated barns (12 x 12 but I have 59 chickens and 8 ducks) with an opening (covered with hardware cloth) running across the top.

If it gets too cold in the winter (0 or below) you can put a small light bulb to keep the air a bit warmer.