Yeah cow manure is VERY wet.

Compare to horse manure which is relatively dry, easy to shovel.

The context was shoveling a barn, and you can't leave it until it dries out, can you? I don't know how often you have to clean a barn, or how long it takes for the manure to dry, but my naive assumption would be that it takes too long to dry for how often you need to shovel.

You assumption is correct. It is scraped out while still wet.

Tangentially, that can be a job for robots: https://www.youtube.com/watch?v=pz4t0qIISTs