For mild winter, would you rather have two set of tires or single set of all-weather?

Hi there, I recently got a car that came with all-season. I live in Vancouver and the winter here is usually not that cold and rarely snows in the city, however, I do go up to the mountain to ski once every week or two usually between mid-December to March. Technically all-seasons with M+S is legal on the mountain road, but I don't feel comfortable about driving up there when it's freezing point, even less so if it's snowing.

So I'm kind of torn right now on what would be a better choice for me. Getting a new set of winter tires means I'll spend a lot upfront on new rims and tires for about $2k. Or I can spend less for all-weather tires (about $1.3k and sell my all-season) but expect to get a new set more often.

Also I don't drive too much, around 12,000 km or 7,500 miles a year.

Any input is appreciated, thanks!