There will still be plenty of free parking within walking distance to REA. Everytime I've gone to a game at REA, I've parked in the medical school lot and it's always been free and there's always been plenty of spots. It's a bit of haul, especially in January, but it will still be a viable option if free parking is your biggest concern. Also, I believe the shuttles from the local bars are free.
I've lived in the Twin Cities for a few years now and I admit that it's kind of comforting to hear people in Grand Forks complain about parking/traffic, even though it's a hundred times better up there than it is down here. People down here just simply accept sitting in traffic half their life and paying whatever is asked for parking. The last time I went to a game at Mariucci, I think parking was $12 and it took me 20 minutes just to get out of the lot after the game.