Could be that it wasn’t smoke that you saw, but as you guessed, water vapor.
The smell could have been coming from a burning car up the road or whatever.
I know that when I first started driving a car, I’d often worry there was something wrong with the car when I smelled burning, but it never was the car, always something outside, so I learned to ignore it. Surprising that it wasn’t the car actually, considering some of the old junks that I (of necessity) owned in my youth
‘ Only reason I can think of that something might begin to burn in the rain is if water is getting into your electrical system causing a short circuit in the wiring, however, all electrical circuits on your motorcycle should be protected by fuses.
So! Just in case, you might want to ensure that all the fuses in your fuse-box are of the correct ratings (check your manual), make sure that none have been bridged with aluminum foil or similar by some DIY “mechanic” (a real no-no) and also ensure that if you have any accessories hard-wired to the battery, that they have an appropriate in-line fuse fitted.
I had an accessory tail/brake light-bar fitted on my last bike and, for ease of installation, had used those splices which have a razor blade in them that cuts through existing wiring insulation to tap into it. Anyway, I eventually took the light-bar off and didn’t bother taping over the slight nicks in the existing wire where the razor-splices had been (the wiring was inside the “sealed” tail light housing after all). Anyway, come Winter, I kept getting fuses blowing. I took it to the dealer and they could find nothing wrong and just replaced the blown fuse (of course the wiring had dried-out by then). Then I remembered the light-bar. I disassembled the tail light housing and put some electrical tape over the nicks in the wiring and voila, no more blown fuses.