As for the original debate on cheap new vs higher quality used, my answer is neither.
After just one winter of use, the heat cycling a tire goes through hardens the compound. Even if the tires lost 10% of their tread, the heat cycling can significantly reduce performance. So it's not just how much tread is left, the compound also matters.
My problem with cheap tires is they offer piss poor performance all the time (wet-dry-snow-ice), and they don't last long.
My problem with used winter tires, is that they are only really good until there's about 60% of the tread left. After that, they're about as good as a cheap new tire (generally speaking, of course there's difference with make and model of the tire). However, you may enjoy better wet-dry performance with a used higher quality tire.
I always run my winter tires for two winter and then sell them and buy new ones...