The fiber and protein is still there, but the sugars get washed away. So given a free choice between rained-on hay and green hay, animals pick the hay that is sweeter.

Still, it will have the fiber (with some shift from ADF to NDF), most of the carbs and most of the protein (like 90 to 95% of the non-rained values).

Were I a livestock producer, I would use the rained on hay early in the winter, when the metabolic needs of my cows were lower than they will be in late winter (third trimester). You want your best feed going into the cows/ewes just before they calve/lamb to get the milk production up and the body condition maximized.