This is my first car/current and it's been a blast if you don't mind outrageous insurance rates haha
If you aren't down with the finance game like me, there's a lot of fun little cars you can get in that price range. If I was in the snow I'd personally buy an SUV/Truck. Maybe an old 4x4? I have an old Nissan Pathfinder that i picked up recently for no particular reason other then it could be cool in the future. Just to name a few; Jeep Cherokee, Jeep Liberty, Nissan Pathfinder, Nissan Frontier, Toyota Tacoma, Ford Ranger.
Just filtered 4x4/AWD | >100,000 miles, on auto trader and came up with some really good options. You're not in california so no point in sharing links but; (I have no idea what the market on these cars is like so i'm not sure if the prices are high/low for the what they are)
Used 2006 Subaru Impreza 2.5i Sedan for $6,299
Used 2004 Jeep Grand Cherokee 4WD Limited for $7,675 Used 2005 Volvo XC90 AWD T6 w/ 3rd Row for $5,995