It's an interesting fact that when it snow it's normally warmer than when it's sunny in the dead of winter. Snow is 32 degrees, and the cloud layer tends to act as an insulator. When it's clear, radiational cooling can produce temperatures in the negatives numbers. Temperatures rarely get that cold when it's cloudy.
Only if the ambient is 32°F. If it gets colder, the snow gets colder. If it gets warmer, the snow turns to water. It does tend to snow less if it is below ~10°F. But that is because the dew point of the atmosphere has been driven low (i.e. little moisture left in the air).
Snow does have insulating properties that slow the transmission of heat through it. I believe that is mostly due to the amount of air space trapped inside.