/\ what he said.
All seasons aren't as good as a summer tyre in the summer, and not as good as a winter tyre in the winter, so are a compromise not worth paying for.
I had the cross climates on an Alfa 147 years ago and they were only slightly better on snow. Absolutely no comparison to their full fat Alpin winter tyre.
FWIW, the PS4s with reasonable amounts of tread remaining are actually really grippy down to 2 degrees. I've been very impressed with their cold performance.
You're always going to be better off with 2 sets of tyres unfortunately. If safety is your primary concern, get proper winters. Find a cheap set of 16" steels on ebay. You don't need expensive 18" winters. Yes 16s are a bit squidgy in the corners when it's +8 or warmer, but when it's properly cold, icey and snowy, you will thank yourself for it. Taller, softer sidewalls help with traction on compacted snow.