It has the potential to not determine the team which plays the best football, but he one who is most used to the weather. That isn't what the championship game should be about. They all may have to deal with some weather to get there, but it is patently unfair to have Miami to have to play a championship game against Green Bay in weather like they had in Philly. They are giving Green Bay an advantage which has nothing to do with which is the better football team.
I'm saying this from the point of view of one is adamantly opposed to domed stadiums. I agree with you in general that football should be played outdoors. But when it comes down to teams which play most of their games in such completely different climates, the playing field for the championship game should be leveled as much as possible or they have failed in their intent to determine the best football team.
Why is being able to adapt to changing conditions not part of finding the "best" team?
Being able to play in bad weather is a skill. Since half of the NFL regular season is played when the northern half of the country is cold and potentially snowy, not building a team that can handle the elements should have the chance to be punished.
Think of it this way: Every NFL team is built primarily to play in their home climate. Indy (or St. Louis, or Detriot) can afford to have more long-play receivers and speedy running backs, because they play at least half of their games in a dome and several others in warm weather. You can say the same thing about Tampa or San Diego. Teams in outside, northern climates (Green Bay, NY, New England) have to build their teams to play a bunch of games in cold weather outdoors. Power running backs with surer hands and shorter passes.
As long as the Super Bowl is played primarily in warm climates, the NFL is rewarding the prior set of teams, because those northern teams haven't played their entire seasons with the ability and roster to run to the outside and throw it deep.