Generally no, you should not ski with glasses.
Skiing with glasses can be dangerous, with or without Over the Glasses goggles (OTG). A crash on the ski slopes could result in broken frames and glass in your eye.
Glasses also tend to fog up because of the temperature difference as well as moisture levels. Fogged up glasses are hazardous as they disrupt your vision, making you unaware of your surroundings. Without a clear vision, the chance of colliding into another skier increases.
Some skiers prefer to wear contact lenses under their snow goggles.
However, contacts can get rather uncomfortable in cold, dry climates. As soon as you hit the slopes the cool weather will start to dry out your contact lenses. This leads to irritated eyes and blurry vision, something no one wants to deal with while skiing.
Over the Glasses goggles aren't the perfect solution either.
OTGs push your glasses into your face so they stay secure when you move. But this extra pressure can get uncomfortable real fast.
Additionally, when wearing OTGs there is a high chance that your glasses or goggles will fog up, or even both. For a skier, this inconvenience can be enough for them to take the whole thing off, putting them at risk of an injury.
One solution for this is to use an Anti-fog solution, which prevents your glasses from fogging up for a few hours. Anti-fog solutions can be had in spray, gel or single use wipe forms.
A better option would be to use prescription ski goggles.
Prescription ski goggles ensure that your eyes will remain completely protected. Some can be customized to your exact prescription, giving you the clearest vision possible. Prescription ski goggles are especially important if you happen to have myopia, hyperopia, astigmatism or prism.