NEVER spray cold water on a hot engine.... It can be bad for electrical components and metals don't really like being taking from One extreme to the other, (hot to cold)
Surging is caused by a lean fuel mix ratio, meaning there is either TOO MUCH AIR in the mixture or NOT ENOUGH FUEL in the mixture.... This could be the result of a leaking carburetor/intake gasket or even a cracked intake pipe (manifold).. Or if the fuel line falling apart internally bits and pieces can flow into the carb and plug things up blocking fuel.
Post the engine model numbers so we can see what particular set up you have, should be stamped into the Overhead valve cover at the front of the engine.