Players do perform differently in certain weather conditions, but that is simply not enough.
Teams and players should be given weather ratings.
For example, the Miami Dolphins would have a terrible cold weather rating, because they play at home in sunny South Florida. They would perform worse in December in New England than the New York Jets.
However, teams like the Buffalo Bills, who are used to playing in cold weather, would have a terrible hot weather rating. They would fatigue easier playing in hot weather.
Quarterbacks that play indoors would have a tougher time throwing in the wind in places like New York and Chicago.
Stadiums should also have ratings based on volume, loyalty of fans, historical significance, etc. Teams would get flustered more easily playing at Lambeau Field than playing at Jacksonville Municipal Stadium.
Historical stadiums like Lambeau would also give the Packers a slight statistical boost when they were playing at home, and even more-so if they were playing a rival at home.