The only downsides to freezing film:

1. It takes space. My wife routinely makes comments about how full our chest freezer is.
2. You need to warm your film before removing it from packaging (ziploc bags, canisters, foil wrappers, etc.). The rule of thumb is 4 hours to ambient temperature, though if you're going outside in winter to shoot it, it might be a little shorter.

Slow emulsions keep nearly indefinitely if frozen. Faster ones keep better enough to still justify the bother. Refrigeration is better than nothing and a good compromise for film you will use soon but not immediately.