Collect everyone's share upfront, before you book the cabin and the lift tickets, into one place held by whoever's planning. The group sees who paid and where it goes, so the planner never fronts the mountain.
A ski weekend is three or four costs stacked on top of each other: the cabin, the lift tickets, the gear rentals, the drive. One friend usually books the house and buys the group's passes on her card, then spends the week before the trip texting six people to send their part, some of whom "forgot their card at home."
Most of the cost is known upfront, but a ski trip also has the running expenses you can't total in advance: the lodge lunch, the extra day pass, the grocery run for the cabin. Instead of one person fronting each one and requesting everyone back later, collect a little extra into the table at the start as a shared kitty.
Then whoever pays for a group thing requests that amount from the table, the planner approves it, and everyone sees it come out. Nobody keeps a mental tally, and whatever is left at the end is right there on the record to send back evenly. (Renting the cabin itself through a host? See handling road trip costs for the on-the-way expenses too.)
The planner holds the money the way she always did, the difference is that now everyone sees every dollar. The money goes through Stripe to the planner; TableCash never holds it and is just the shared record.