I would look at a pair of good quality hiking boots AND some over boot traction like yak tracks. I have a pair of waterproof Merrell Moab 2 Mid that have pretty great traction on their own, plus they are waterproof and the thick sole helps keep my feet warm and come above my ankle so if I happen to step funny I'm not breaking an ankle. They aren't extremely heavy, but are definitely not as light as a sneaker, unsure if the weight would be an issue.

They are affordable enough that you can get away with wearing them daily if you're just walking around, but durable enough to last a few seasons. I've had mine 3 years running and they are in great shape. I bought a second pair for hiking cause those get beat to shit but even those have lasted more than 2 years. Every "winter boot" I have bought previously looked nice, but either didn't keep me warm, didn't provide traction, or fell apart too quickly.