This is a difficult questtion, depends on a lot of things- like how deep is the snow, traffic, hills and so on. If we are thinking just you, the children and the bike I would say that if you on your bike have a serious skid or worse the child is safer in a trailer.
If snow is deep maybe see if you can fit bigger wheels on the trailer, like 24". I`d go for fairly narrow tyres. Look at the "extrawheel" trailer. I think it uses a 622 wheel. I`ve used both 650B and 622 wheels on trailers on dustroads and rough terrain.
Also there is a time to ride in the trailer and a time to leave the trailer. At five yrs (like Bat56 said his son is) maybe a BF tandem or something similar is going to work better? Forum members has reported on children riding in the trailer for several years until the parents find it really hard to keep pulling them around, and then refuse to leave the trailer and ride a bike. On a tandem or similar a young child can get used to riding the bike, can enjoy the feeling of being able to help out with getting around, and also it is easyer for the child to stay warm. This way you get at least some help and you only have to deal with the rolling resistance of two wheels in stead of four. Children grow so fast, and they like to help out and feel big and strong.