We live in Nebraska, and I do know that your weather can be colder than here, but our 7#er prefers the cold over the hot. She loves snow. We don't take her out much, but she likes to potty in the snow. She prefers snow over rain.
We have had no problems. We don't use a sweater or coat when she goes out to potty cuz she is not out very long. We put a coat on her if we take her places. If it is really cold, -0, I keep a sweater on her in the house. We visited my daughter in Minneapolis over Christmas once, and Sophie had a sweater on the whole time. She did just fine.