The rule of thumb I use is to blow a hole through the ice if it has been solid for a week. (YMMV - We usually have freezing and thawing multiple times here in Ohio.) I have shallow water air sources present for Winter use, so as not to eliminate the warmest 39 deg F water at the bottom of the ponds.

Dirty/snow covered ice is worse as it lets almost no light through for photosynthesis.

If you have electricity further from the pond, it is cheaper to run air to the pond than electric. I use 1" plastic water pipe to send aeration about 650ft to my second pond.

There are a great many Winter aeration threads here that can provide multiple perspectives on the subject for you to consider.