The amount of power you can get from your vehicles engine to the ground can be the limiting factor in how well your car performs on the road in slippery conditions. Owners of 4 wheel drive cars can attest to their superiority compared to the more common front wheel drive models usually found on American roadways. When it comes to maximum traction in less than ideal conditions it's hard to beat a well engineered all wheel drive system like those found in Audi or Subaru cars.
Thankfully for those who live in regions given to inclement weather their has been a major expansion in the number and quality of all wheel drive models of all types in the model lineups of many auto makers. Where as four wheel drive systems in the past required more bulky hardware which added inefficiencies by default, modern 4x4 systems are typically nearly as adept at squeezing the maximum out of every gallon of fuel at their two wheel drive counterparts. Of course there is usually still a price premium to contend with if you are looking to buy an all wheel drive model.
Audi is considered a pioneer in the AWD vehicle market and has included their Quattro drive system on many models since the 1980s. If you are in the market for a good used all wheel drive vehicle it would probably be worth your time to check out the Audi lineup to see what might fit your needs.
Probably their most popular models are the A4 and A6 sedans and you can find any number of these cars for affordable prices in the pre-owned market. If you are looking for a small, fuel-efficient car that can get you around in slick winter conditions and maintain maximum traction on wet roads the A4 would be a great place to start. To pick a model year as an example let's look at the 2002 model A4. It features a turbocharged 1.8 liter engine that puts out 170 horsepower. Not earth shaking, but nice for a small car especially since the torque curve starts low at just under 2000 rotations per minute. Of course the best thing is that this car is equipped with the Quattro AWD system and you can still expect to get over thirty miles per gallon during highway driving. According to KBB you can expect to get one of these 2002 models in great condition for around $8,000.
If you need more space than the A4 has or just want more power you could move up the Audi model lineup and look at the popular A6 which is also an all wheel drive model and comes with either a 220 HP 3.0 liter V6, 250 horsepower 2.7 liter turbo-charged V6 or a big 4.2 liter V8 that puts out 300 horsepower. Naturally the model for the fuel economy minded driver is the 3.0 liter V6 but if your primary focus is on the traction system any of the models will suit your needs. Although the V8 model may bring more you should be able to find a great 2002 model year A6 for under $9,000.
So there are your two suggestions to get you started in your 4 wheel drive car search. You can branch out and explore other models from other auto makers or you could even look into the full size Audi A8 or if your budget allows move up into more recent model years if they have features you would like and are willing to pay more for.