Most importantly-a wool or acrylic hat that fits over the ears, and waterproof mittens/gloves.
+1 to @LeastComplicated Sierra trading post is the go-to place for reasonable high quality clothes. Watch for on-line coupons. There have some stores too.
One thing I would recommend in addition to warm clothing is a full-spectrum lamp. I’m from Colorado (the land of cold yet sunny winters), and the biggest shock for me was how dark it gets in the winter in Mass. The lamp helped a ton during the grey, dark days. I can only think it would be even worse coming from California.
These are all so helpful! I hadn’t even thought of some of these things before they were brought up, thank you!
As someone who also moved from a tropical climate to western MA, I definitely agree with many of the above suggestions. A couple realistic things however: (1) you will acclimate to the cold, and (2) most people don’t want to look like they’re prepping for an Arctic expedition every time they step outside in the winter, so I wouldn’t necessarily recommend breaking out your biggest coat the first time it dips below 40. I have two basic “sets” of winter clothes–the winter clothes I generally wear to get between classes are less warm and a little more stylish–a wool coat and insulated leather boots or rubber rain boots (get something waterproof unless you want a shock stepping into slush); an underlayer or two (long-sleeved cotton t-shirts are fine–no need for thermals), and jeans. Leggings under the jeans (once again ordinary cotton/lycra blends are fine) will keep you a lot warmer if you need that. You’ll want to dress in layers for class because a lot of university buildings are heated very warmly, so you’ll want to be able to strip down to a single long sleeved layer on top. However, if this is your first experience with snow, I’m guessing you’ll want to try out some snow activities! For that you’ll want some thin underlayers, a heavy parka, and big chunky snow boots. These will also come in handy in the event of a snowstorm or truly frigid weather.
I’d prepare and try to buy stuff online now. A lot of companies are running sales on their winter stuff, and most offer free shipping if you’re buying more than a certain price point. As mentioned above, REI, LL Bean, and Land’s End will have really nice stuff, although REI is more of an outdoor company. Also be sure to check eBay for deals on lightly used items (I’ve gotten a couple of bargains on coats on eBay). The North Face is a very common company among college students. Patagonia is expensive, but generally higher quality than North Face; they also have a focus on sustainability and are fair trade, if that’s something you consider when buying clothes.