Agreed to with preacher. Vintage would be fun but it may not be practical enough for a college student in the northeast. Below are some answers for a later model if you are also considering buying one of those.
No you haven't lost your mind, I'd say you're just coming into the right frame of mind

I have a few friends with Grand Prix and although I love Mustangs, I wouldn't bad mouth a Grand Prix by no means. They are a bit more luxorious and the last time I checked they weren't too slow either >> not a bad car in my opinion. But lets not be irrational here, nothing is better than a
Stang (more a statement of passion rather than fact) :shiny .... Anyways I'm a college student as well and I too live where snow is a possibility everyday for about 8 months out of the year, so I understand a lot of your concerns.
If you can get 6-8K for your Grand Prix I'd say that you shouldn't have any problems finding a decent
stang. The first thing you need to do is decide which models years are the most appealing to you. When you decide which years you like best, shop around, do some research on this forum(and any other resources), and then decide if the models you like fit into your budget. For 6-8K your best bet is to go 98 or older I think. It is possible that you could find a 99 or newer for this amount, but theres a good chance that it will be a V6 (again, decide how much power you need). I got my 1996 GT, no rust no damage, good paint, runs great, etc(check my pics) for 4700$ from a guy in Michigan and I'm sure theres plenty for sale especially during the winter months. That brings about your first question:
1.) How are they in the snow ? Not too many people brag about their mustangs awesome winter performance so it's likely that your Grand Prix would be at least a little better. Personally I like fwd in the snow but I couldn't stand the thought of salt slush oozing off my fenders so I dont drive mine in the winter. I live on campus so I dont need a car at school, but if you do need daily transport I'd suggest waiting the winter out with the Grand Prix or purchasing a winter rat for the season. If absolutely necessary, get some awesome snow tires and keep that baby as salt free as possible.
2.) MPG for a mustang is the same as any other car for the most part, meaning your Grand Prix wouldn't necessarily win by a landslide. It depends on how you drive. I've gotten better than 27 mpg outta my GT but outta the same car i would have no problem getting it below 12 mpg (such as when a friend gets in for the first time and you have to show him/her why they should get a mustang too). Plain and simple, if you drive responsibly you can get good gas mileage, but if your always high in the rpms your gunna feel it in your wallet.
3.) Insurance. I'm pretty sure that mostly depends on your provider and your specific stats. People ask how I afford it being 20 years old with red sports car. I only pay 45 a month for basic liability and around 100 with collision, fire, theft, etc. Drivers education classes, defensive driving, day time running headlights, abs, car alarms,..all those things should help to lower your insurance to a reasonable rate. As long as you dont have a lot of points on your license your insurance will be afforadable.
4+5) Common repairs and faults ? Thats gunna depend on the model and year that you choose, I haven't been around enough of them for long enough to make any comments here. I'm sure there are some moderators and gurus in here that will provide some helpful info for that issue. What work I have done, brakes, exhaust,some electrical, cai, etc is pretty basic and shouldn't be a problem as long as you have patience and some guidance from a book or friend.
Hope this helped and good luck in your search.