Weather can certainly affect players' performances, which would inherently affect your fantasy football team. With that being said, you shouldn't solely draft based on weather. It wouldn't be logical to take Kirk Cousins, who plays in a dome, over Josh Allen, who plays home games outside in Buffalo, NY, because of winter weather in NY.
It is important to keep an eye on weather on a game-by-game basis when making start/sit decisions. RotoWire's Weather Report is a useful tool in identifying where weather could have a negative influence on fantasy productivity.