In reply to Robin Woodward:
We paid by card in the Torino last month, having checked on the website in advance that they take cards.
Having said that, I wouldn't have a problem carrying the cash if necessary. Just remember where you packed it! And take plenty spare for incidentals if that's a possibility. The coffees, beers and snacks quickly add up...
I do wonder what happens if you find you can't pay the bill? We got a bill for far more than we were expecting in the Ecrins last year (our own fault, bad adding up) and only just managed to pay after scrabbling around for 5c pieces. I wonder if there's a facility to pay in the valley, or do you have trek back up having visited the cashpoint?