How should a buried water hose be winterized?
You should definitely blow out the water to winterize. Anything in that hose will definitely freeze. There may be enough space in the line to get lucky and make it through a winter, but it'll eventually ruin that hose and replacing it looks like it would be annoying. They make adapters for air compressors to do this very thing.

You can rent or borrow an air compressor and use something like this to connect (sometimes called a blow out hose or blow out plug)