Whether it's cultural or a sign of changing times, I don't know, but when I was growing up, it was never even considered, let alone mentioned. You kept your shoes on, except in your own home. Period. Certainly, if you had wet feet, you used whatever mat was provided for wiping feet, and if your shoes were sufficiently mucky that that would not do the trick, you'd offer to take your shoes off. But the default, if you will, was to keep them on.
Nowadays, I know that some people prefer no shoes in the house, and will take my cues from how my host is clad, and whether there's a collection of shoes near the door. If it's at all uncertain, especially if there's a gorgeous pale carpet spreading before me, I'll enquire. But if the norm in that particular house is clearly "keep 'em on", I don't think another thing of it.
When people come to my house and ask if they should remove their shoes, my response is "however you're comfortable is fine -- we don't bother, but feel free to, if you prefer."
Umm...I didn't vote, because none of the options really fits.