All natural shelter here, but one or two fields have pig arks and we do let the ewes with young lambs use them.
All hands-off, natural lambing, outdoors in April, here (Shetland tup). We have covered pens we can use if any family needs a bit of extra tlc, but since we started using only the Shetland tup and lambing after mid April, no-one has needed it

We had some unexpected late lambs one year, so the lambs were only 2-4 months old going into winter. We opened up a back way into the haystore for them and their mums, which was much used and appreciated. But older lambs only need additional shelter in very wet years.
Cold isn't a problem, but they need dry to lie on. We spread straw in the field if necessary to make a dry pad for them to lie. But if the rainfall is incessant, then a field shelter, or access to a shed, is a boon.