Best way to avoid disappointment is to sell parking spaces online in advance.
Season pass holders get first dibs and people buying 3+ lift tickets get the parking space for free. That would encourage ride sharing. It would also be apparent that folk should plan to head somewhere else if they can see the carpark is already booked out.
Not a bad idea! Although the argument of how many days per decade this is actually an issue does come to mind.
Could also instigate a snowsock/chain only policy when snow is hitting. Booking a parking space could include provision of snow chains which the parking charge would fund.
I don't have much experience with chains but I believe a given set fits a narrow
range of tyre sizes? In that case not practical to hire them out probably (if I'm understanding you correctly?).