what do you think would be cheaper, getting just winter tires to fit the 17" rims (if possible on the s2000) or getting cheap 16" rims with snow tires?

 

If you already have the rims, then just get the tires. This would be cheaper than getting 16" tires AND another set of rims (even cheap ones IF you can find cheap ones you like). If you already have 17" rims, you must still have your stock rims, right? Why not put the snows on them?

 

i sold my stock rims

 

Oops!
The trouble with not having a second set of wheels for the snows is that twice a year you have to take the car, tires, etc and get them changed over and balanced - a real pain in the rear. You might get the wheels scratched or they might jack hammer the lug nuts on or ding the car when it's with them (I just hate think about it). With a second set, you can change them at home at will. Sometimes, if we get a Chinook (a warm wind that turns winter into summer-like conditions for a few days or weeks, I'll flip rubber. I've gotten it down to an art now and I can do a change in less than half an hour, sometimes in as little as 15 minutes.

 

Agreed, always better to have your tires on separate sets of wheels. Saves a lot of money in the long run, too (in balancing/mounting costs).