In reply to mutt:
Okay... I'll bite.
Ski touring and ski mountaineering are skiing. What's the problem?
The other part of this revolves around how you define "responsibly". If anything can only be "responsible" if it has no environmental impact, then you're right, you can't ski. Then again you can't drive, buy phones or computers or fart. Don't ever light a fire or ask your friends to come and see you unless they walk or cycle. You almost definitely need to opt out of modern life. Your life becomes rather limited, if pure.
Conversely, if you get the train to the alps, go to resorts who rely less or not at all on making snow, in countries with more environmentally friendly power generation, and in life try to reduce your carbon footprint and be as environmentally friendly as possible, then you can, as this fits a more normal understanding of "responsibly".
Post edited at 12:07