Once the harvest is in, is it necessary to keep settlers assigned to the Farmer job, or can I assign them to other jobs during winter?
Farmers aren't needed during the Winter. Once the harvest is complete they will be assigned to the laborer task behind the scenes until spring arrives. This behaviour isn't exclusive to farmers though. Any villager who has no work to perform in their assigned job will act as a laborer until they have work to do relating to their job (i.e. if a blacksmith doesn't have the materials to make tools she'll act as a laborer until materials are available).