"The rate of sustaining an injury while skiing or snowboarding on Swiss slopes was 2.8 per 1000 skier days on average from 2008 to 2010. The fatality rate was 0.7 deaths per one million skier days in the same period of time."

"In cars, one person died per 5.5 million passenger hours traveled."

So skiing seems 4x more dangerous.

Anecdotally, I've read that one hospital in the Swiss Alps was struggling money wise, because the ski season was ended early, and ski accidents were a major revenue for them.

According to [1], Skiing is 0.7 micromorts, whereas driving is about 400km per micromort. Therefore, the break-even point is 140km (0.7 * 400 / 2 way trip). If your local ski resort is < 140km away, the skiing is more likely to kill you.

[1] https://en.wikipedia.org/wiki/Micromort

That's per day of skiing, and a lot of ski trips are more than one day.

This doesn't take individual behavior into account though. A lot of people are skiing more cautiously than the insane risk takers who kill themselves in avalanches or falls in deep woods or backcountry. Also, the driving to the ski resort is likely to be more dangerous than regular driving because you're more likely to encounter icing, snow on the road, and low visibility conditions.

All in my guess would be that the driving is more dangerous for most skiers.