I was looking at the screw in felt pads the other day and wondered if they would be a good solution for floor protection. The ones I was looking at have a felt pad that the manufacturer attached to a metal piece then put a screw through both. You then take the piece and screw it to the bottom of the chair leg with the metal part against the wood and the felt to the floor. This might seem like a good idea at first, but what happens when the felt either flattens or wears down. You then either have the screw scratching the floor, the metal piece scratching the floor or both scratching the floor and you can bet that they’ll do more damage then just a bare wooden chair.
When you are looking at floor protection products have a think about the consequences if a part falls off or the felt delaminates. Sometimes it's just not worth the cheaper options. Have a look at the Flexi-Felt clear range for a product that will stand the test of time and looks.