I was curious, so I did some looking. I didn't find anything definitive, and nothing on college football, but here are a couple analyses.
Sports Illustrated: Looked at NFL data 1985-2011 and did not find any advantages for northern teams in cold weather, nor southern teams in hot weather. Article did not give actual numbers.
Reddit: Found higher win percentages for home teams in cold weather games (<32 degrees and <20 degrees) in the regular season than the historical home winning percentage (57%), but also found a lower winning percentage for home teams in cold games in the playoffs. This analysis uses less data, so there are smaller sample sizes, especially for the playoffs.
A real analysis of this would include strength of teams, which neither of these links seem to do. For instance, if you're looking at the 2000s and 2010s, the Patriots and Packers might skew the win percentage quite a bit by being two of the teams most consistently playing in cold weather while also consistently being two of the best teams in the NFL over that period, regardless of weather.