I don't have anything novel to say. I live in the snow belt. I have hardwood floors and so do my neighbors and friends. Outdoor shoes get removed upon entry and some form of indoor foot cover is substituted.
This is of course a guideline, and if someone is unprepared, or uncomfortable, we forego this and allow the outdoor shoes to remain. My floors are easy to clean, and eventually will need to be refinished no matter what I do so I don't get too crazy. I have a 60 pound dog. He does more damage to the floors in a day than a few weekend guests with snow boots covered with a residue of salt and sand.
Oh, the same works when I go to friends homes, I definitely take off my shoes. I carry warm and fun socks to wear.