As for Minnesota's gameplan - Bridgewater WAS completing short passes, you're correct, the problem is that you need 10-15 plays just to get into position for a field goal, in conditions like that it's difficult to move the ball upfield, and in fact, Minnesota's points game from 2 drives that started in our half, and another drive that started on the MIN 46 that was immediately followed by a 15 yard rushing the passer penalty on 1st down.
The final drive Minnesota actually threw the ball downfield somewhat, completed one and had another extended due to DPI.
Throwing the ball long in that kind of game was EXACTLY the right idea, because you complete one pass you pretty much guarantee yourself a good shot at 3 points, given the game was always going to be low scoring, complete 3 or 4 of them and you're in a good position to win the game.
On the other hand, you could complete 17 short passes like Bridgewater did and go absolutely nowhere all game, because he really needed to complete 25+