My thoughts would be a large class C, but a good size A would be better. In my hunting for MH, I realized that a C is still hard for the DW to get up and out of the passengers seat while moving. I think with all of your live stock an A would provide them a little more room. If I was you I would be looking a class A.
I could be wrong, but I believe you will still need to winterize your rig. I do not believe there is a true all season rig that you can just leave the water in and get up and go. Maybe if you kept your rig plugged in with furnace running etc. you may get by. I would check with the folks up in your neck of the woods for that information.