Here in FL Feb/March is usually dairy goat kidding season, though there are exceptions. It's later farther north. Most breeders sell between 2-3 months old, unless they sell bottle babies, then it's earlier. So, I say try in spring.
Not necessarily. A lot of northern breeders still kid out in February and March to take advantage of the lack of parasites. Snow and ice on the ground mean that most parasites are inactive. So by the time spring makes things warm and wet, the kids are a bit older and have stronger immune systems. Of course, there is always the chance of a doe doing something silly and dropping her kids in a snowbank*. BUT most breeders will also put does who are due to kid in a dry, draft free barn.
*A breeder I know had a doe start kidding unexpectedly and early, and did just that! All the kids, PLOP! right in the snow, and no effort to dry them off. Thankfully the breeder discovered them pretty quickly, and all the kids recovered from their chill without any problems.