Keep outdoor sessions to an hour or so, warm up indoors, then go again. A sled (pulkka) is easier than a pushchair on snow.
Dress children in thermal base layers, a wool mid-layer and a snowsuit, plus balaclava, mittens and warm boots. Check cheeks and fingers often for white patches, a sign of frostnip. Pin reflectors on coats in the dark, never let children onto river ice, and book a car seat with any transfer.