IMHO the best you can get is a Mitas with Winter Friction compund.
Mitas has a variety of models.
Ordinary trial-tyres doesn't work well, they clog up with snow and gives no grip.
I use Mitas XT454 (with 7mm studs) for enduro and XT644 (with 1.5 mm studs) for mixed driving. XT644 is also used by the Norwegian and Swedish army. I've also tested XT644 without studs and it works pretty good.
Mitas XT644:
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