As you can see, we live in a similar climate, and we have trained ours to go outdoors. She doesn't seem to mind snow at all. We just take an extension leash, open the sliding glass door (as we stand inside

), and she runs out to do her business and comes back in. It works great unless the grass is wet

. Then we find surprises in the house (poop!!!) Anyway, she does fine in all conditions. We just don't leave her out there any longer than it takes to do the poo or pee.