You can pick up a 92-99 bonneville SSE/SSEi with most to all the options for under 4K. Parts are fairly cheap, the interior is decent, especially with the 9 way power seats. 96-99 SSEi has the Series 2 supercharged motor which has plenty of power, and they handle well in the snow. I drove a 93 SSE for the first year of driving, and currently have a 93 SSEi.
Also, a buick regal GS, 97+ are good in the winter. Has that after the first bonneville and it loved the snow. Plus you can get heated seats. THe GS also had the Series 2 Supercharged motor.
If you want cheap to buy and fix, I got a 1998 Lumina LTZ that I used last winter. $2000 takes it this weekend. I added heated seats to it and they work decent. I have that posted somewhere on here.