Sometimes the dogs are wet. The kennel runs have drains in them and waste is removed by spraying water into the kennel and flushing it down the drain. Some shelters remove dogs and dry the runs with a big squeegee. Sometimes shelters put dogs on the other side of the kennel by closing a drop door, and then spraying. And sometimes shelters just spray the run.
No matter which way they do it, the dogs get wet to varying degrees.