In the "Hoogtelijn", the magazine of the Dutch Alpine Club NKBV (don't laugh, 70.000 members and growing ) there is an interesting article on CO₂ emissions of overnight stay in a hut of the Swiss Alpine Club. Most likely this info comes from the SAC magazin (would be interested if someone could share that original article itself).
One overnight stay emits 4.6 kg CO₂ (comparable with a 14km car ride or 180km by public transportation).
Main contributors:
38% logistics (transport goods to/from valley)
34% (preparing) foods and drinks
In 2040 SAC wants to have the huts completely CO₂ neutral.