Sanding a badly splintered wood floor?

I think you're probably on the right track, although without actually seeing the floor perhaps you should get professional advice from a restorator (other than simply a floor refinisher)

I say this because old floors tend to be alot thicker than modern ones, and it is possible that yours could be salvaged.

Listen to Judith S!!! If there were no stains and the finish was poly, and not wax you have the option of screening. To see if your floor is in good enough condition find the most worn area and drop a couple of drops of water on it. If the water beads up and does not soak in, the poly is in good enough shape to screen. Screening- Go to your local Home Depot or tool rental store. Ask for a 15" to 18" orbital floor sander (Screener). It looks just like a floor polisher. Tell the rental folks you are screening your floor. They will give you the correct "head" a pad, and 100 to 120 grit sandpaper. It will cost about $60-$80. Take the machine home. Practice first by using the pad only, to get a feel of the sander. Then attach either the 100 or 120 grit sandpaper and make 1 pass across the entire floor, that should be enough. Then screen the corners that the orbital sander could not reach by hand. Return machine, they cost money. Clean the entire area except the floor with a shop vac and a wet rag. This also means walls, cabinets, lights anything dust can attach to. Now clean the floor with a shop vac and a tack cloth. If you use water you run the chance of raising the grain of the wood causing a poorer finish. Come on you have already come this far don't cut corners. Now that you have everything clean. Time to finish. Time to choose a finish, the finish should match the original (water or oil based) but I perfer oil base because of the golden color it brings. Waterbase has the advantage of not smelling as bad and drys faster. Use a flooring finish like Varathane (No I don't make any money from the plug) it will pay off. When choosing a type of finish High Gloss will show any sanding imperfections but looks beautiful if finished right. Satin may be a better choice for a beginner but doesn't shine like a hardood floor should. While at Home Depot pick up a lambs wool applicator and extention handle. (Saves on the back) Back home, apply the finish thinly with long even strokes always keeping the edge of your working area wet, will keep down on streaks. Wait until it dries and recoat. If this is too much info I appologize. If you are in Colorado Springs give me a call and I can take care of it for you.

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That floor is at least 3/4" thick.

Sand it until it is smooth again. It is definitely worth saving and laying carpet over it would be a crime.