These are called ski-bikes. A few places rent them, mostly resorts that cater to Texans. They've been around for about a decade.
I don't think it's much of an issue over whether to allow them, as I don't think anybody actually buys them, it's just something to rent to gapers. So, unless the resort chooses to rent them, they're effectively banned.
BTW, my understanding is that Vail has them, but only allows them on certain trails and at certain times. I'm not eager to share a hill with them, since an out of control person on a ski bike can do some real damage carrying that bike frame. But I have, and I've survived.