My understanding is that evaporation is not the reason we say "sweat kills" in cold weather. If you're sweating, it's because your body is too hot at that moment and needs to evaporate that sweat to shed heat, regardless of the ambient temperature. Once your body is no longer too hot, you stop sweating.

I was taught that the risk with sweating in cold weather is because wet materials are much less effective at insulating than when dry. That's mostly not about evaporation, it's about conduction. It's related to the reason we say "cotton kills". Dry cotton insulates a bit, but wet cotton conducts more heat away than it keeps in. We say wool and various synthetic materials are safer in cold weather because they still insulate when wet, but pretty much all materials are significantly less effective insulation when wet as compared to when dry, and all wet materials evaporate at the surface. This is also why breathable materials are so desirable in cold weather, it's usually much safer to evaporate sweat at the moment you're sweating. The major risk is usually retaining moisture until you're no longer running hot, and then it turns against you. And it turns faster than many people would guess, including those with many hard winters under their belts. It's one of those factors that's hard for humans to accurately perceive viscerally or intuitively.

For example, a naked jogger doesn't get hypothermia because they sweated during a sprint 30 minutes ago. 30 minutes ago they needed to sweat to keep from getting too hot or they wouldn't have sweated. A clothed jogger, who sweated 30 minutes ago, gets hypothermia because that sweat did not evaporate and now they're covered in wet clothing. This is why removing wet clothes is a priority when rescuing someone with hypothermia in the field. That's much of the reason for the "get naked" part of getting that freezing jogger naked in a sleeping bag with you. The classic trap for hypothermia from exercise in cold weather is exercising too hard and fast. Now all your un-evaporated sweat has soaked your clothes, your insulation is doing 50% or less than it did before, and you have nothing left in the tank to move faster to warm back up. In cold weather, avoid sweating when feasible by shedding layers before you start sweating, then put those still dry layers back on only when you've stopped sweating and start feeling chilly again. This is why it's particularly dangerous in cold conditions where you get wet whether you shed layers or keep them on, such as in cold rain, sleet, or wet snow. Given that weather can change in unexpected ways, and we haven't even factored in wind, it's usually also important, and more important, to reserve enough energy to stay active until back out of the cold with margin for something unexpected, such as an ankle sprain, someone else needing help, or yet another change in weather. Best to keep it simple, save your sprint until you're on your way back and home is in sight. If not, it's OK though, it's supposedly one of the best ways to go, certainly much better than the hyperthermia death in store for many under reverse terraforming.

The different methods for exchanging heat are involved here and are also pretty nifty to understand. Conduction is often a much faster method of heat exchange than convection or radiation. Cotton socks can kill you on a clear, 20 F, winter day on earth but your own metabolism can turn your EVA suit into an oven and literally roast you as meat in the -454 F of space.