I have never ridden a trike but have had quite a few sidecars over the years but never in the snow but the famous Snowbum BMW mechanical guru (
Snowbum, Snobum, BMW motorcycle repairs, Airheads, Oilheads, Classic K-bikes, prostate cancer ) used to. His very, very long biography is quite amazing and worth a read despite the challenging rainbow text. A true Polymath!
Robert Fleischer, snowbum, snobum, Full biography try the novelette it takes a while!
Sidecars are heaps of fun but can be quite disconcerting at tmes especially on off-camber left handers for our Aussie/UK versions with chair on the left, especially when the chair goes skyward and you keep going straight ahead. A bit of weight transfer and muscle is required at times if no 'passenger*' onboard the chair (*the correct term is 'ballast'). I used to get on preferably wide gravel roads hit the brakes and do 360's down the road for fun.
Very simply for our versions they turn left around the fulcrum of the 3rd wheel by applying power to the back wheel and turn right by braking and the weight of the chair swings around the bikes centreline assisting right hand turns. The weight can severely decrease normal brake performance and traction or the lack of it is part of the tool set for riding.
There is a large number of experienced bike riders who try one once only after scaring the crap out of themselves when they head straight out of control towards some large obstacle.