I recommend Rusutsu ski resort for the one day. They have great terrain and its big. They also have a hotspring at the resort and a hotel with bars if you want to relax after skiing.

http://www.best-of-sapporo-japan.com/rusutsu.html

Theres also a free bus that takes you to and from the resort from Sapporo.

For restaurants, I think eating soup curry is perfect in the winter. check out this link for soup curry restaurants around Sapporo.

http://www.best-of-sapporo-japan.com/japan-food-1.html

Enjoy