Donal,
Realistically, April 1st through October 31st (NW Connecticut). Southern Ct. has courses that stay open all winter if there is no snow cover.
There is a course south of Albany, NY ( Hudson River Valley) that also stays open, weather permitting.
Anything north of Albany NY, Springfield Ma., Worcester, Ma., is ordinarily closed after October 31st.
If you want to play golf in comfortable weather during the months of January and February you really need to be in Florida (preferably S. Florida).