Moved to a new place but can't get my car here for another couple months. Tired of bumming rides/walking. The immediate area is dense enough that I can cycle to and fro without issue. I don't know much about bikes. I'm new to cycling and have been doing a fair bit of research, but still can't pin down a specific brand/model. Can you help?

I need a beater to commute on that can handle ice/snow and gravel/dirt roads. It snows from October until April here and they salt the roads here like a mofo, so corrosion is a problem. Any ideas? Specific features to look for?

Budget: $500