Hi, nellee. I can't think of anything worse to put on your hardwood floors except maybe a couple of very large old dogs. The water that you put in the clay pots will migrate down into the floor, causing, at least, white water marks. Over time the white water marks (water in the finish) will progress to black stains, then rotting of the wood and delamination of the plys in the plywood. Somewhere along the way, you will have to replace the floor, which will not be covered by the warrantee, so it will all be at your expense. The other bad thing that will happen is that the sun will fade the stain on all the floor except where you left the plants. There is not much you can do about that except pull the drapes.
Fortunately, help is at hand and cheap. Our local plant stores (Frank's Nursery and Crafts--and I'm sure that there are many others) sell clear plastic saucers to protect the wood from the water and catch any drainage. These are really cheap but they work great.
Remember that it's not good for your plants to have their feet wet all the time either so don't put in any more water than the dirt in the plant can absorb. When you do water, take a towel along with you to pick up any drips from the watering so they don't stay on the floor either.