I'd attack the splatters individually, first trying popping the splatters off with my thumbnail. Scraping it carefully with a hard wood or plastic scraper might also work. Craft-type exacto knives also have different blades that could be used, though the metal blades stand a better chance of cutting the floor finish.
Wiping the splatters first with mineral spirits might help soften the paint, but could also soften the floor finish so should be tested first and not left on for an extended time.

I ditto Randy's advice. I always pick them off with my fingernails. It helps to have a wet wash cloth to scrub with a bit first.
Too bad about the splatters.
Renee

Try rubbing alcohol (isopropyl) or denatured alcohol.

Neither should bother a cured polyurethane finish.

Thanks for the advice. I'll give it a try tomorrow.

To make matters worse, the paint is right in the middle of the floor. Didn't notice it because an area rug was covering it.

Jane