Yes, I really would think so. When it is really cold I think that any one would really have some sort of negative impact in their game. It might not be a huge negative difference, but it would still do something to affect the way that any one would play.
Living in Michigan is a skill. At first, when winter rolls around, you are cold and always want to put on a coat. But after about two weeks it's like, "Only 5 below zero? Ha! I can run out and get the mail in this sweatshirt!" The Lions are used to the cold just like the rest of us who live in Michigan.
Weather is around us, we feel it and it can certainly brighten or darken our day but that does not mean is the correct reasoning for why anyone would believe that the Detroit Lions play worse in the cold weather. That is a false assumption and would require extensive research.
Any professional sports team must be prepared to play under any reasonable weather conditions and for that matter, under any reasonable conditions period. Football is no exception; it is quite the contrary. Football is a sport that is played when weather conditions, including cold temperatures, can be at their diciest. Unfortunately, the players signed up for that when deciding to become Detroit Lions.