Denatured Alcohol will remove dried latext paint from varnished surfaces usually without damaging the sheen of the varnish. The longer the paint has been there, the longer it will take to disolve it. If it does damage the sheen, another coat of varnish can be applied, just be certain that all paint has been removed before you revarnish. Any paint left on will be permanantly entombed in the varnish.
The Alcohol should be tested in an inconspicuous place first to see if the alcohol will leave white stains in the clear finish. If that happens, your into total removal of the finish and refinishing of the wood.
There are latex removers like "Goof off" and "Klean-clean" and a couple of others, I've never found that they work any better than alcohol, and they smell worse too.