There are 2 products that I know of, specially formulated for this. One is called Goof Off and the other called Oops. They may or may not work, depending on the paint, and they may or may not removed the varnish, depending on the varnish. The both come in a small can, similar to a 'lighter fluid' can.
If the floor has modern polyurethane varnish, the finish will be safe. And if the drops and spatter are latex paint, they should be able to remove it. Unfortunately, the only way to find out is to try it. Maybe you can test a hidden area to see if it hurts the varnish. Then, if not, go ahead and try some of the paint spots.
Good luck, and let us know how it works out.