No, they are not lighter than air. The water droplets, which are more than 1000 times denser than air up high, can float because of aerodynamics. The updraft can produce upward forces to hold the tiny droplets in vertical air movements. What's more, the horizontal wind can produce lift on the droplets with the right shape like an airplane's wing. Thus, the droplets can float as long as they are small enough and there is enough air movement. 
The droplets can also float in another way. When droplets get too big, or the air movement drops and down they come. And as they descend into warmer air they start to evaporate. Smaller drops don’t make it to the ground. So clouds can actually also exist as regions where tiny drops are continually forming, then falling, then evaporating again, with the bottom of the cloud marking the height where they finally evaporate away.
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