The answer is yes. Low temperature does affect resin and plastics and could cause your doll to crack while traveling in transit, or in storage where the climate gets low. To avoid breakage, try not to ship dolls where they will travel in or through areas with freezing temperatures. If the location of a doll has climates of snow or ice, it's possible that in transit even to a warmer climate that through transit or as it moves from warehouse to warehouse destination it could crack or break on its own or become brittle enough that basic handling can crack it. This makes winter doll shipping tricky, and you might want to wait until temperatures warm up if the doll is expensive.

Vinyl dolls don't seem to be as fragile and won't break just due to cold alone, but storing in freezing temperature can cause vinyl to become brittle over time or attract moisture.