I lived in Sweden for several years and biking with small children was very common. I never heard of a child being harmed by the cold air. While we were there, I routinely walked my older children to school with the youngest in a stroller with moms and babies whizzing around me on bikes and with strollers. Babies were out in the cold, often in bike seats.
Children can tolerate the cold quite well with warm clothes. My children had excellent cold weather gear -- quality long johns, a good wool sweater, an oversuit, mittens, boots, and a good hat -- they were bundled and very comfortable.
Goodness, get them out! My kids loved Swedish winters, they beg to go back.
We did hear of two cold weather deaths, but both times it was someone who got drunk, passed out on the way home from the pub and died in the snow.