Searching students is time intensive and keeps eyes on the larger population at Hogwarts. It would make it easier in the long run for the true culprit to continue on.

It is an adult behind this all, obviously. Snow is either protecting that adult or also uncertain as to which teacher it is. Seeing how they follow through with these new rules and making it seem his suspicions are elsewhere may be a ploy to draw them out.

Snow could be on the side of good here and his methods might be simple diversion tactics.

There are a great many variables to consider.