I also live in MN and i know of 2 people who have outdoor pools (and 1 with indoor, but that was built in his basement with the house, so different story) that have just heated the hell out of it during the winter.
Pool 1: Guy has an electric hard-top retractable system, so he hits a button, and a hard insulated cover comes out over the pool. You can walk on this cover, etc. It's awesome, and I'm sure quite $$. However, he keeps his pool heated 365 in MN. His is not covered at all, just in his backyard. I think with the hard top, it insulates better. Yes it will cost more in electricity to heat it during the winter, but it probably won't cost as much as basically rebuilding the structure around the pool. If he wants to go swimming in the winter, he hits a button from his house, the pool top retracts, he wraps a towel around himself, runs outside, jumps in the pool, and is good to go.
Pool 2: Tried heating her pool during the winter. It worked, but her first Xcel Energy bill came, and it cost her like $400+ to heat her pool in November/December. After that, she stopped doing it.
I honestly think that you could get away not enclosing the space, and just heating the pool. Obviously, you're not going to use it when it's -20 degrees like it was last week here, but if you get a good insulated top on the pool, and your goal isn't to throw pool parties (and just swim laps like 1x a day), the amount of time with the hard top off the pool will be very small.
Have you been to/heard of Bluefin Bay on the North Shore? They have a soft top mostly uncovered hot tub and pool they leave open year round, and people are using it right now, I'm sure. I am 80% sure they are using Geothermal heat for their pools though, so that would save some money. Drilling a geothermal well for the space would likely be FAR less expensive than completely remodeling the space.