Intuitively the conductivity explanation sounds more credible. Also, my experience is that cold damp air doesn't immediately feel colder than cold dry air. The difference is that, over time, it feels like it leeches the warmth out of you quicker, which would make sense if it was conducting heat away faster.
Moontanman, you said "I've seen ice condense directly out of the air twice in 40 years of living near the ocean and seeing cold wet air". Where I come from in East Anglia, this phenomenon happens at least half a dozen times every winter. It's called hoar frost.