I've heard of cases and also personally met someone who survived with a full recovery after they were taken to the hospital after being found unconscious in the snow for (presumably) more than 45 minutes, and claimed their temperature dropped below 0 degrees (Celsius) after they recovered in the hospital, though obviously I can't go into their medical records and verify that temperature. What mechanism allows someone to survive being so cold for so long, particularly if there is a lack of oxygen to the brain, and if someone can survive it for that long, why not indefinitely like for cryogenics?
I'm no medical expert by any means, so it's possible it's a combination of things of course, but for references the first being that a doctor telling me first hand that it's possible, but rare for someone's pulse to stop in frigid temperatures and still recover after more than 10 minutes with a lack of oxygen referencing something about the decomposition of tissue slowing down, and then also news articles like these that I don't have any particular reason to doubt given the consistency of such a story across different venues, which also suggest something about frigid temperatures allowing people to survive injuries, oxygen deficiency, or tissue damage for a longer than normal time.
I'm not completely sure about the lack of oxygen part of the question because it kind of seems like they evaded that part of the question, but they definitely said frigid temperatures delay the decomposition of tissues in someone's body and suggested someone could survive longer due to that, and I don't know why tissue decomposition would be a problem unless someone had already lacked oxygen for a long time to make them susceptible to it.
I remember the old saying "better cold and dead than warm and dead," I guess this makes sense for when you find someone unconscious.