I have no idea if the frigid temps will help or hurt the Patriots or the Chiefs more. Or if it will help or hurt the offenses or defenses more. Here are the coldest games in NFL history and the outcomes:
Dec 22, 1990, at GB (2 degrees) - Lions 24, Packers 17
Jan 15, 1994, at Buf (0 degrees, -32 wind chill) - Buf 29, LA Raiders 23
Dec 26, 1993, at GB (0 degrees) - GB 26, LA Raiders 0
Dec 10, 1972, at Min (0 degrees, -18 wind chill) - GB 23, Min 7
Dec 3, 1972, at Min (-2 degrees, -26 wind chill) - Min 23, Chi 10
Jan 28, 2008, at GB (-4 degrees, -24 wind chill) - GB 31, Det 21
Jan 4, 1981, at Cle (-5 degrees) - Oak 14, Cle 12
Jan 7, 1996, at KC (-6 degrees) - KC 10, Ind 7
Jan 10, 1982, at Cin (-9 degrees, -59 wind chill) - Cin 27, SD 7
Dec 31, 1967, at GB (-13 degrees, -48 wind chill) - GB 21, Dal 17
So the average score of these games is 22.8 to 12.1. Scoring was lower in those days, but still, I would suspect that we could conclude that these would constitute lower-scoring games. So I'll suggest that the cold weather is going to hamper offenses and help defenses. I suspect it's just harder to grip the ball, throw the ball, kick the ball, and catch the ball, which are all offensive things. On D, all you really need to do is tackle and run and deflect the ball (not necessarily catch it).
So if the original line is 57.5, if the temps are going to be between 0 and 5 degrees, the play would be to take the under.
Now if that's so....which team does it help more - NE or KC? Both teams are in what we'd call cold weather locations, as KC absolutely has games as cold as Foxboro.