I used 15/32 4X8 4IN OC FIR T1-11 Fir Plywood Siding on the outside of my tractor. I primed it, caulked the seams, and painted it so it would shed water better. I used only 2x2 studs trying to reduce the weight. I screwed and glued all the joints to strengthen them knowing they are going to get racked each time I move the tractor. I was sorely tempted to use the nail gun for assembly as it is quicker, but opted for deck screws and wood glue for increased resistance to the racking. If you use 16 inch centers on your framing it will be plenty strong, but somewhat heavy too. You may not want to use 2x2 studs as I did, as it will reduce the insulation space by half. Since I live in south Texas, insulation is not high on my list of worries. My tractor is 4x14 feet, and is all that I can do to move it without the help of a lawn tractor. BTW, sheathing adds a LOT to the rigidity of the structure just make sure you fasten it every 6 inches so it doesn't pop off the studs when it gets racked.
My tractor is not complete yet, but the chickens are in it as I had to get them out of my garage! Here is a side shot of my yet to be completed tractor: