If you need to refinish the floor then I would just consider sanding the whole thing with a floor/drum sander. This will sand/grind the heads right off, then after rough sanding use a nail set to tap what is left of the nail shanks down a little so you can fill the hole with filler. Do any filling just before the final fine grit sanding so that any extra around the holes will be removed and not show up in the final finish, some folks fill after the first coat dries, then screen off excess, then keep coating - this way your filler won't soak into the wood and leave a stain. My guess and worry is that if you try to "pull" the nails that you will create a lot of damage, both from the actual prying and from the ring nails coming back up and leaving large splinters as they come back through. If the heads are small then I would take a heavy duty nail set or pin punch and just drive them down below the surface. If filled correctly you shouldn't be able to notice the filled holes when the floor is done.