When a receiver slips and falls, then the QB has to look to one of the other 3-4 options. When a defenders slips and falls, then the offense is probably gaining something like 20 yards, and often a TD. Now it means the Pats can't lean on routes where the ball is in the air before the WR cuts, but they can work around that.
Also, a nice layer of snow greatly limits what the defensive linemen can do. If teams can't rush Brady, then it's just a matter of time before he finds someone that's open. The Pats, more than most teams, look for guys that can win as pass rushers even if they don't win with their first step. A lot of teams aren't the same way, and preventing their star pass rushers from getting that big jump off the ball is enough to ruin their production. Chandler Jones, for example, uses his first few steps to set up his next move (usually slapping the hands followed by an outside move), where a guy like Brooks Reed goes for the outside arc right away and isn't nearly as good at countering if he doesn't get the angle right away.