Does Speed Gro work on Winter Seeds?

SpeedGro makes your crops grow 10% faster. So with winter crops that take 7 days to produce, it will reduce the grow time by 1 day (assuming that it will round up from .7 days). In your case, using SpeedGro still won't give you enough time to produce a harvest in the 4-5 days you will have leftover. Don't worry about not producing anything in those 5 days, you can of course still be productive by using these days to mine or upgrade your farming tools.