Mini's and Bmw 325's will Nickel and dime you to death, a used Mini or a used Bmw cost a lot of $$$ in maintenance and repairs and of far-far from, being reliable.
An SUV or 4X4 truck are great in the snow,The Op seems to want a car for the winter and that's fine, may I suggest a Volvo S40 in fwd or Awd these car will fly throw snow and ice, great on gas and will last 200K miles with basic maintain done on them and can easily be bought in the price range the the OP is looking for.
Yes the Mini and the Bmw are great driving cars, so is my Porsche Boxster and my Lotus Elise, but with all the snow we get here in Michigan they all suck in the winter.That is way I have Volvo S40 R and a Jeep wrangler.