The issue of climate change adaptation becomes increasingly important in Switzerland, which has already faced higher than average global warming during the last decades. Winter tourism is expected to be one of the Swiss sectors most at risk from climate change mostly because of the increase in snowline altitude. In fact, several studies predicted high climate change costs for this sector. However, most of these studies have largely overlooked the role of adaptation in alleviating those costs. We tried to fill that gap with a better modeling of climate change adaptation in GEMINI-E3 which is a computable general equilibrium model. Future snow cover variations are derived using different climatic scenarios from the European ENSEMBLES project. By 2050, we find rather moderate welfare effects of a decreasing snowpack with costs ranging, for the Swiss economy, from 24 to 122 millions USD which represent a 0.01% to 0.03% decrease in final household consumption.