An audi would be expensive to find any parts for even though the older ones are rebadged volkswagens. Cars are generally less expensive and in better condition for the money because trucks hold their value, so you can find a "nice" car for $1000 rather than a rust bucket 4x4 truck type vehicle. Subarus are plentiful and cheap and fulfill what you're asking for and they also get good gas mileage.
I had an '83 mercury zephyr (shares "fox body" platform with mustang) with 2.73 gears, open diff and the gutless 3.3L auto combo and that thing was HARD to make lose control in the snow (i had snow tires though). With the long wheel base and open diff it was very steady in the snow, although i never got into a situation where i need to go uphill from a stop. Good luck finding something!
After i get my '89 GT my '84 LX will become my snow car
, i don't know how well that will work out, probably not very well but it's what i've got.
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'84 Mustang 5.0 LX
My car