Wool breeds have enough lanolin that in winter the rain does not get through their wool to the skin. Some wool breeds grow extremely long fleece which ends up parting in the middle along the spine. Those one or two breeds are at risk of getting pneumonia during the winter (rarely) since the icy rain can get onto the skin and run along under the wool. This is rare since very few sheep grow wool that long.
Normal wood breeds have no problem staying out in rain and snow. However there have been rare occasions when a spring blizzard will blow in after shearing. This happened in the late 1800's in Utah when about 80% of the sheep flocks on pasture froze to death with their lambs. It also has happened that storms will hit and sheep that have not been shorn before lambing will stay out in extreme temperatures. The ewes, having plenty of lanolin rich wool, won't feel the icy temperature and seek shelter so the lambs freeze to death.
Hair sheep have a lot less lanolin in their wool, and a lot less wool. Then they shed it out in the spring. While Katahdins shed completely, some some Dorpers retain a mohawk strip along their backbones. This is acceptable for Dorpers since in South African sheep can get severe sunburn on their spines.
FYI: In my grandmothers' and great grandmothers' times there were no rubber pants for babies' diapers. And no disposables either. Instead you would knit various size diaper covers on very fine needles with wool. Then those would be boiled to shrink the wool. Once that was done the wool diaper covers were essentially waterproof! My grandmother told me that years ago. She also went to visit her mother- and aunties-in-law on their farm in Iowa. My uncles were still in diapers and since they only did a boiled wash once a week, she was appalled that they just took the wet diapers, laid them over the bushes to dry out, then put them back on the babies until washday arrived when they boiled them up. She was a city girl and accustomed to having a laundress available as needed. Amazing what people can do when necessary.