Haha. What? I've lived in Cambridge with a car for 2 years now. No problems. If you want to bring your car, go for it. You will have no more trouble than you would find in any other northern metropolitan area. In fact, speaking just for Cambridge, I have been surprised with how easy it is to find parking.
Now if you're going to have a car in a town other than Cambridge, I'm not as knowledgable. My girlfriend lived in Brighton and parking could sometimes be a pain. It all depends on what neighborhood you're in of course, but like I said, that's like most major cities in the north half of our country.
It is definitely true that a bad snowstorm can cause havoc. Make sure you own a shovel, and it helps to have AWD. If you have the money and it's worth it to you, rent a garage spot. Protects your car and avoids a lot of the snowstorm headaches.
Driving into Harvard square and parking during the day on a regular basis without a Cambridge permit will be extremely expensive, I would guess. The HES parking permits start at about 5pm, you will probably need to hunt for metered spots before that. Won't be a stress reliever at that point.
I hear ya, though. I could have probably survived without a car for these two years, but it can be a form of stress relief, as you said, to be able to just jump in the car and go somewhere.