It depends on the manufacturer’s cleaning and maintenance instructions. It is vital to carefully follow the maintenance instructions to ensure the maximum lifespan of your jacket. If the care instructions do not say anything about no machine washing, then it is most probably safe to wash it in the machine.
However, it would be best if you always wash your ski jacket separately without any other clothing piece that might damage the jacket. It is also important to empty all the pockets and zip all the pockets and jackets before throwing it in the washer.