How well do Apple Watch it can handle cold?

Apple Watch is designed to work best in ambient temperatures between 32° to 95° F (0° and 35° C), and should be stored between ambient temperatures of -4° and 113° F (-20° and 45° C)

If you want a slightly cynical opinion, the watch will be at the same temperature as your forearm and it is unlikely you will let your arm get to the temperature extremes which can be tolerated by the watch. The display might become a little sluggish, and the battery capacity might be slightly lower than at comfortable temperatures, but the watch will survive and probably work better than an iPhone kept in a cold pocket.