There are a variety of important features that your leather jacket will lack compared to a ski jacket. Borrowing or buying a ski jacket from a thrift shop would definitely be worth it.
Skiing is pretty physically intense. If it's not very cold (above 20?), you'll sweat, and most ski jackets don't actually have much insulation as they're designed to block as much wind as possible, while still being breathable to let some sweat out.
Leather will soak up water if you fall, your inner layers will get wet with sweat, and it will not be long enough or cinch tight enough at the waist to keep snow and cold wind from going up your back, which is extremely uncomfortable.