How high is the percentage of the population suffers severe depression due to rainy, gloomy weather?

Depends: When looking at the entire us population the average is about 4-6%. Since you are in new york, your state's percentage is likely higher.

That depends on: where one is geographically. "SAD's prevalence in the U.S. ranges from 1.4% in Florida to 9.9% in Alaska.[5] " See: https://en.wikipedia.org/wiki/Seasonal_affective_disorder **** In other words - the percentage is variable.