Hi, Jac. If you have real hardwood floors with the varnish in good condition, you should not have too much trouble. You might get some white marks but you should be able to get those out, if necessary. You might consider getting a big rag rug to catch some of it--yeah, like the dogs are going to wipe their feet, right?
If their claws have scratched thru the varnish, then you might have trouble and that's a big job to fix, so keep an eye on this. If the damage is not too bad, you can sand with a floor buffer and old sanding screen and apply another coat of varnish. If you have "engineered flooring", you will have more problems and sooner, but it should not be too bad with real hardwood.