As long as the ambient air temp is tolerable for you, you can compost. There are different methods of composting, including hot and cold composting. Hot compost requires more attention but happens at a faster rate, cold composting is fine too, it just takes longer to reach a final state. The heat in hot compost is the result of bacterial action, not surrounding air temp. That said, if your temp is 30 below zero, achieving and maintaining hot compost through winter would be a bit of a challenge. But once the temp is reasonable, maybe 40°, you should be able to hot compost too. I'm referring to actual compost piles, not a couple of inches of mulch. A couple of inches of mulch isn't likely to heat up.
I don't know what fish mulch is, not a common thing in Ohio. But generally any organic matter can be used as mulch. You might want to keep it a couple of inches away from existing plant stems to avoid damage.
What is fish mulch? Does it stink like fish? Drawing critters with fish smell could be a problem, those critters might be anything from rats to bears....
Karen