According to my Californian dormmate back in college, it’s bad. Frequently exclaiming “how can you people stand this??” level bad.
Despite being a New Englander since birth, I hate being cold so I’ll give you some pointers.
If money is an issue, your coat is what you want to buy new since the lining deteriorates over time. Get one long enough to cover your whole butt, not a waist length jacket. Ones that allow you to adjust the tight/looseness of the waist are best, because while you’ll want it loose enough for a heavy sweater to fit under it, you don’t want it hanging off you. Extra airspace between you and the coat makes you colder.
GoodWill and the like will have tons of sweaters, often brand new from donations of overstock by LL Beans. You’ll want sweaters in different weights. From Halloween to around Christmas, and then from sometime in March until it finally hits the 50s, you’ll be happy in light weight sweaters. For the rest of the winter you’ll want heavier sweaters, and make sure they’re loose enough to slip another layer under it, be it a t-shirt, or thermal underwear, or under armour because it’s often too cold for a sweater alone to be warm enough.
If your current jeans are not warm enough, there are two options. The first is to replace them with flannel-lined jeans. The second is thermal underwear under them too. Both thermal tops and bottoms are sold in the underwear departments of stores, and they should already be there in Boston stores since they’re in stock here. With slacks, you’re pretty much stuck with thermal bottoms under them since lined slacks are not commonplace.
You need hats and gloves. If you have to do any shoveling, make sure you buy several pairs of gloves, so you change them when they get wet - they take a long time to dry. A scarf might or might not be useful to you. If you’re going to be shoveling, or walking by the water, or just spending a lot of time outside in general, I’d pick one up.
They sell boots that are thermal-lined, usually leather. You might want them. Those, coupled with thick socks help keep your feet warm, even if you need to trudge through snow and slush.