I personally thrive in the winter - if I'm "in charge" of a thermostat, I always check with other people, lest I freeze them out of the room. I'll never complain outwardly that it's too warm, because I know 99% of the time, it's a "me thing". That said, they've been keeping the Garden FREEZING lately, even for me. Possibly a combo of the cold weather and complaints/problems with the ice? The loge is way colder than the balcony (where I am), and obviously row 1 will be colder than 15 - you're not only farther from the ice, but heat rises. If she's a Patriots fan who's been to Gillette, you can tell her it's DEFINITELY not that bad.
For me, a jersey and a warm long-sleeve shirt is plenty warm - the layers help. The most practical thing for a cold person would be t-shirt, long shirt, sweater/sweatshirt, warm jacket, and a hat. I do keep an uber-heavy jacket that could theoretically double as a blanket under my rear end for the game, but only because JJ has completely ruined the walk from the T to the Garden.
A throw blanket would probably be allowed if they can search it easily, but I don't think it'd be super practical - the seats can be cozy, and you may be getting up and down if you're near the aisle. The Pro Shop sells Celtics blankets online...so if they have it in the store, they can't really keep you from bringing one into the arena, right? I've never seen one at the Garden.