Most courses around here, NE/Central Massachusetts, close Thanksgiving give or take.
That leaves:
Lots of choices for indoor/outdoor/covered/heated ranges.
Usually play a few rounds on Atkinson CC's simulator.
Windham CC and Far Corners do their best to stay open year round (I absolutely love playing Windham in the Winter).
I have never gone down to play but I hear some courses on the Cape also try to stay open year round.
Also do what a lot of others have posted, putting drills, chipping drills, mirror work, ...
Never feel golf deficient during the winter, just the opposite, I rather enjoy the peace and quiet. Played today (Crystal), forecast was for snow flurries this morning and tonight, no accumulation, saw a twosome finishing the 18th when we played the 2nd and that was it all day