Yes, lightning does occasionally occur during mountain snow storms. It is usually quite surprising for the skier. The snow storm lightning may light the sky with a curious diffuse white light. The reason lightning is so uncommon is that the type of clouds and weather systems that produce a lot of lightning do not develop often during the winter. They are clouds produced by the heating of the ground and cold air aloft - a condition more common in spring and summer.
Lightning is produced as thunderclouds produce the classic big billowy shape.
These type of clouds have strong up and down drafts, mixing positive and negative electrical charges. Lightning is a result of an imbalance of electrical charges. Lightning is mother nature's way of balancing the charges out. Sometimes the lightning is between clouds or between the cloud and the ground. Lighting is a dangerous killer.