At this time of year the snow covered roads can be extremely dangerous. The snow itself can be slippery, but it can also cover ice, meaning that a stretch of road could provide reasonable grip followed by a patch of sheet ice which could not be seen due to the covering snow.
Good driving lessons, although they can obviously not cover every possible scenario, should at least touch on some of the potential hazards that a driver could realistically encounter in a normal year. Ice and snow are certainly some of the more likely and dangerous hazards any driver will be likely to face.
So, what can be taught? The first thing about driving in harsh weather conditions is skid avoidance. How to drive in terms of speed, steering, braking, cornering etc. The big problem is simply grip. Where there is ice there is simply not going to be enough friction between the road and the tyres. Therefore it is best to avoid, as much as possible, scenarios where you are likely to need to heavily rely on grip.
Secondly there is the matter of how to deal with skids when they do arise. Removing the cause should be the priority. If the skid has been caused by harsh braking for example, then ease off the brake. If the loss of traction has been caused by harsh acceleration, then ease off the gas. There is much techy stuff involved with skids, so the best person to provide training would be a suitably qualified trainer.