The type of plastic may be relevant; most are more brittle at lower temperatures, but some are more affected than others. So while the impact forces may be same as off a skate, the capability of the helmet may be reduced if it’s well below zero.
In the same way that the courts reduce the damages for a biking head injury if not wearing a helmet, they would probably reduce them if skiing in one not designed for snow sports.
So I wouldn’t say your helmet is unsuitable, just not as suitable as it could be – and better protection than no helmet. Unless there’s some reason, eg, insurance conditions or resort/snowpark rules saying you MUST wear a helmet, it’s entirely up to you how much risk you’re happy with. I wear a kayaking helmet for skiing.