That was a great observation to help us all feel better about the animals and the weather.... snow on their backs... thank you for sharing that... it makes perfect sense now... :)
Briskly rubbing the head, neck, and shoulders to stimulate good blood flow in the calf is how we were taught to treat a mildly chilled calf, we used clean bath towels that had gotten worn or thin and washed between uses. If you use a calf warmer with heater and fan and enclosure, be sure to get calf out before it is too warm and calf's brain is fried. Also, never warm milk or milk replacer above 105° F, so proteins are kept intact. If too warm, proteins are denatured and calf will get diarrhea.
