Can one assume atmosphere (primarily nitrogen) is heavier than water (vapor)?
Yes, humid air is less dense, but temperature and pressure are much bigger factors in the density of air.   Temperature and pressure are what drive updrafts and wind speed and direction much more than watervapor. 

Absolute Humidity, or, the mass of water vapor in air, is a smaller factor.  See here for more detail.

Temperature

a 5° change can vary air density by almost 2%.   That means that the Sahara desert (35° c) and the North Pole (-25°), with humidity and pressure being equal, the air in the North Pole is about 24% denser.  Locally, if we assume a 15° variation daily or 25-35° variation yearly, that's 5%-14% locally, give or take, based on temperature.

Pressure

Per Avogadro's law, a 10% increase in pressure, everything else being equal, corresponds to a 10% increase in gas density.  10% variation in air pressure is quite a bit (unless you're climbing a tall mountain).   Locally, 10% variation in air pressure is rare, unless you're looking at records.  Daily/Weekly highs and lows in barometric pressure might vary air density by 3%-7%, ballpark estimate.   See some record high and low pressure here. 

Water Vapor

Again, using Avogadro's law, if you add 1 water vapor molecule to the atmosphere, and maintain temperature and pressure, you need to push one other gas molecule out of the set volume, so per cubic meter, increasing humidity does displace some of the heavier gas molecules, so there is some lightening of the air, but the effect is quite small.  Water-vapor has a molecular mass of 18.  Our Oxygen-Nitrogen atmosphere has an average mass of about 29.   But Water Vapor rarely takes up more than 1% of the atmosphere, perhaps 2% in hot climate, 3% in very hot, but that's 3% of the air with a 38% decrease in mass, resulting in a net change of less than 1% in the most extreme conditions.  You'd be unlikely to see a variation of as much as 1% density by water vapor alone, outside of a very rare event, like a thunderstorm over a desert.     

There's other factors for wet air, such as the evaporation of water has a cooling effect, so as water evaporates, the local atmosphere cools, so mid day when sunlight driven or wind driven evaporation is at it's peak, it's not quite so neat and tidy as to say that evaporation makes the air lighter, cause the cooling effect of evaporation may actually make the air slightly more dense, not less dense.  It's only less dense if you keep everything equal, but the cooling effect of evaporation doesn't keep everything equal.   

That said, however you look at it, water vapor is likely an order of magnitude less important for air-density than temperature and pressure.   It's relevant enough to pay attention too if you want to study air-density carefully, but temperature and pressure are the two big factors.

A possible exception to this is when there's fog.  Fog contains tiny water droplets which are small enough to be suspended in air by wind, and those individual droplets are much denser than atmospheric water-vapor.   foggy air, under the right conditions might be the most dense air, but in a sense, that shouldn't count, it's like counting sand in a sandstorm as part of the mass of air.  

((Corrections welcome if I made any errors)).