I don't have info on exact weather conditions for these games, but at a minimum games in these locations in January are going to have high probabilities of being cold (at a minimum).
2001: @ Pitt (Win)
2004: @ Pitt (Win)
2005: @ Den (Loss)
2013: @ Den (Loss)
2015: @ Den (Loss)
2018: @ KC (Win)
So, for road playoff games in cold-weather cities, Brady is 3-3. He is also 0 for Denver and undefeated elsewhere.