If a tenant slips on ice, am I liable?
You can be named, and a lease assigning clearing to the tenant is evidence rather than a shield, especially for common areas. It is the most likely liability claim on a mountain rental, which makes the limit on the policy worth looking at.
Can I make it the tenant’s job?
You can assign the task in the lease and it is worth doing plainly, stating who clears what and how promptly. It does not fully remove you from a claim by an injured third party, and it does establish what was agreed, which matters.
I live hours away. What should I do?
Arrange somebody local rather than relying on getting there. An intention to handle it yourself is how properties end up uncleared: the tenant thought it was yours and you were not there. A contractor is cheap compared with a slip claim.