Speaking from someone belonging to a club 1/2 mile from the ocean on Boston's north shore...I think it's a total crapshoot, depending on freeze and thaw in the latter half of March.
In the last say 20+ years that I have been eagerly awaiting our opening date...we have opened twice around 3/15, and once (2001) as late as 4/25. The benchmark is 4/1, and we can usually open without carts around that date. Tough to graph the opening date being earlier due to climate change, etc. as there are other factors, namely getting enough seasonal labor signed on in March to prepare the course to open...perform cleanup, remove covers, etc.
Being close to the ocean means our microclimate is milder than 10-20 miles inland, as the ocean never dips below 34-ish degrees.
One quirk in Massachusetts is that many of the coastal public courses will be open in the winter provided there is no snow on the ground...especially on Cape Cod. Playing in the winter probably means a shorter course than normal, teeing from a mat or grass adjacent to the real tee, but generally the real greens are in use, and frozen golf is fun in its own way...a pond can be a ground-game element!