It must be a mudcat trait. I, too, have never seen anyone else do it, though I myself always sing when walking, bicycling, etc., and also when driving or working unless there's music playing (in which case I'm usually singing along rather than just singing). I even sing in the supermarket, in spite of the anti-music on the PA system.

I sometimes get a negative response to it, usually just a tense question about whether I sing all the time or whether I'm aware that I'm singing. A few weeks ago someone gave me dirty looks to show my singing was disturbing her cel-phone conversation! How's that for irony?