Everybody also knows that 70% of all photosynthesis takes place in the oceans. If the oceans don’t freeze, you didn’t know as much as you thought you did.
First off, whatever happens in our hemisphere is offset with what happens in the southern hemisphere.
By its name, photosynthesis is photothophic, by degree, and depends on the length of day. So, even photosynthesis in the ocean will be curtailed as the days shorten. Especially where the oceans surface is covered by ice. And then you should consider that sunlight does not penetrate water very well.
Temperature also affects the process and changing temperature affects the process. For each 10 degrees C the water temp falls, the rate of the process is cut in half. The oceans surface temperature is affected by the air temperature. The oceans surface temperature is also affected by radiant heat from the sun which decreases as the sun sinks and the day shortens.