We were recently there skiing and saw someone biking with snow tires. Looked like he rode up a non-skiing trail or service road to the base of King Kong. Don't know if he got further.
If you're asking about mountain biking in the summer, probably fine. In winter that's almost certainly a no to any type of bike on the mountain.
Call to confirm -- but I believe that all types of bike are only allowed off- season.
I've never seen anyone with a pedal bike on the slopes but you can call and ask
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