At 120k, I would bet there isn't hardly a good bushing on the rear of that car. I did my ZX3's suspension at 100k and had to cut out almost every rear upper and lower control arm bolt.
Your shocks and struts are also well past due for a change. Don't forget sway bar links too.
The only problems I have in the snow and ice are how low the car is. It doesn't wander at all. Like Iminhell and sailor are saying, I would make sure the car is in good shape mechanically first.