I drove tractor trailer for many years in my youth here in Minnesoota. Chains have a tendancy to break. When either the main chain on either side of the tire breaks, or just one of the cross chains, they flail around and would cause a lot of damage to your trailer. We never ran chains on the trailer. Only on the drivers.
One thing you must do when driving in icy conditions is plan ahead. don't get into a situation where you must brake suddenly. Slow gradually and use the trailer brakes to slow down when you can. If you start to jack knife, use the trailer brakes to straighten the rig out but don't lock them up. Just apply enough to get control and then slow down gradually.
If you don't have to drive on icy roads, don't!!