On the south side, the nearest hospital is in Nalchik, about an hour and a half by car from Terskol, although there is a small clinic in the village of Azau at the base of the mountain. There are several local Doctors in the villages but they are limited in what they can do to assist. A casualty would have to be taken by vehicle to Nalchik.
On the north side, the nearest hospital is in Pyatigorsk which is close to Mineralnye Vody. To get there would mean driving a 4x4 from base camp back across the river and along the off-road tracks to the road and then to the city, a total journey time of about 5 hours.
In all situations, any payments for use of the snow machines would need to be made in cash and recovered later from insurance. The insurance company can help with the repatriation of somebody from the airport to get home but they would be unlikely to make direct payments to a Russian hospital, so therefore you should expect to pay with cash or perhaps a credit card.