Boston has cold wet winters. The temperature from October 1st to March 31st will range from 32 degrees to as low as the single digits: 3, 4, or 5 degrees. Boston is windier than Chicago so Boston's windchill will drive the temperature down several more degrees. On a very cold day the wind feels like it cuts you like a knife, so cover your face.
It rains a lot in a Boston winter so every thing will be slushy and wet. You have to prepare for an ankle deep slush puddle hiding under the snow when you step off the curb. So make sure your boots are high and waterproof.
So dress accordingly. Dress in layers so you can layer off when it suddenly gets warm, or you enter a warm building. Dress in a waterproof over-coat, as close to a lined rain-coat as you can find, and always with a hood.
I usually carry an extra pair of gloves, wool caps, scarfs, and socks in my back-back in case what I'm wearing get lost or stolen or sopping wet.
Life long Boston resident 50+ years.