Subies are always a solid choice.
I've only owned front wheel drive, and always put out the money for good snow tires. It's seen me drive past spun out 4x4s plenty of times.
Blizzak or x-ice. Don't go for the higher performance ones, they're nice on dry roads, but compromise on snow performance.
Right now I'm driving a mazdaspeed3. Holds gear nicely. The regular hatch with ~120 less HP is probably still a little above your preferred budget, but it's got to be getting affordable enough. There was also a protege hatch.
I probably wouldn't go for a jeep, for the longer drives. I just prefer to be lower, gas mileage aside.
Toyota matrix is also an option. Pontiac vibe is the same car, if the American badge doesn't bother you :)
Other ideas, v70, jetta wagon, a4/6 avant/ allroad