Technology

A ski would be a nightmare. Ski bikes for downhill slopes are one thing, but self-propelling a bike with a ski would majorly suck. The only reason a bike balances is because of tiny steering inputs to the front wheel. If you aren't aware of that, it's because of the geometry of the front fork has been worked out a century ago, so it comes naturally. The greatest proof is the reverse-steering bike experiments. Every time the novice reverse rider starts to fall, they steer the wrong way harder and harder. But then it clicks eventually, their brain reverses, and it works again. The gyroscopic effect resists falling, but it doesn't stay upright on its own forever.

Back to the point. I've skied, I've snowboarded. You balance by rocking and steering yourself. While ski bikes do exist for the slopes, all 3 of these take relatively wide paths to stay balanced Ina mild weave. Bikes do it in a much narrower path because they have grip in the tires. Replace that with a constant slide and it gets dicey fast. You lose the ability to balance any time the front washes out. And to see more of that concept, search "lowside crash motorcycle". The front locks/slides, all balance is lost.

Stick to cleared pathways and at least hard pack snow. Powder is awful to bike through. I've done it. No mortal bike tire floats how it'd need to