My rig handles ok in the snow and on ice. The day I took those photos, I drove on everything from six-inch deep snow to clear roads, to absolute sheets of ice. The rig never slid sideways except when I tried to make it slide. The only real drawback to riding on snow and ice is that you have to push with your feet sometimes to get started, as you only have one driven wheel, and sometimes, it has inadequate traction to get you moving.
Since they were designed for military use, you can get a kit for my bike that adds an axle over to the sidecar wheel, so you have two-wheel drive. It would probably be necessary if you planned to do much riding on snow/ice or on soft dirt. The bike is a former People's Liberation Army (Chinese Army) bike, that has been restored with a paint job to resemble the 38 BMW R72, which was the basis for the sidecar rig the Nazis used in WW2. Later, it was copied by the Soviets and Chinese for their own military use. You can buy the former PLA bikes in China, restored like mine, for about $4000.00, and have them shipped over for about $1000 more. (If you are IN China, and have friends in the business, you can buy them much cheaper. My father-in-law lives over there, and rides an identical bike, with the guys who do the restorations. He bought this rig (freshly resstored) for $1650.00!
They are great fun for little money, in comparison to ther sidecar rigs. But don't buy one unless you enjoy turning wrenches!