As I said earlier, I love gardening with moss.  So, I refer to myself as a moss aficionado, though others have referred to me as Mr. Moss, Mossback, and a moss guru.
   We just came out of winter, so my mosses are happy to be growing again.  However, mosses can tolerate winters here quite well, even putting on new growth so long as it is just above freezing and out of the snow.  The photos show how mosses are great to have even in winter, so long as they aren't completely covered with snow.  The moss just popping out of the snow is Bryum caespiticium.  The one in the container is Dicranum scoparium.  And the rocks have several species growing on them.
I usually take no special care with my mosses for the winter, though I do put as many of my moss containers in a shaded area to avoid excessive sun in case there is no snow.