I've done quite a lot of hiking in various types of snow in trail runners; long distance hikers do this in the U.S. all the time.

That said, I highly recommend that you practice this in a safe environment, somewhere you can bail out from if it's not working for you.

Some will use Goretex socks inside, and I like those fine. What's more important IMO is to check the wool content on your hopefully decently thick wool socks. So many synthetic blends these days, sometimes a pair of "wool" socks doesn't have much actual wool.

Bread bags or some sort of vapor barrier can be helpful. If it's very cold then I'd want that when walking; more typically, it's so I can change into dry wool socks in camp and not get them wet when walking around camp in my wet trail runners.

You might also consider whether your wet shoes will freeze overnight; this too is something to have thought through and be prepared for.

I don't think this is for everyone, and it's certainly not always for me either. If I'm doing a relatively short winter hike or backpacking trip, I definitely prefer waterproof insulated boots!