Nah! As long as they are wrapped up snuggly buggly warm they´ll be fine.
We´ve got loads of snow at the moment. When I take Sam out, he has his normal clothes on, then a fleecy jacket, with a hood, a woolly hat on and then his snowsuit, with the hood pulled up as well. He´s like a michelin man and can barely move, but at least he´s warm. He´s usually in the car anyway and just going out in the cold between shops, but if I take him for walk, I have him in the pram lying on a fleecy blanket, with another blanket on top and then the pram cover. He´s not whinged about being cold and is always warm as toast when I take all the layers off.