I don't think cold floors actually come into the equation - IMO it's more a matter of being aware of how sensitive our feet are to any possible sharp "nasties" on any floor that might cause damage/infection if we step on them and are not aware that we've done so. One good reason to have our feet checked regularly.
Robbity
ETA Actually, thinking about it, wearing shoes or slippers won't automatically prevent damage to our feet, it's possible to get stones, grit, etc, in shoes or rubbed heels from badly fitting shoes, and equally well not be able to feel the effects.