How important is dust to making it rain?

This week's question comes from Daniel Wren in Ottawa.  He asks:  

Is it true that inside every raindrop or snowflake is a speck of dust and that the dust is mostly from space? Also, what would the Earth's hydrological cycle look like if there was no dust in the atmosphere?
 
Bruce Sutherland, from the Department of Physics, Earth and Atmospheric Sciences at the University of Alberta explains that rain cannot form from water vapour alone because it takes an enormous amount of energy to overcome the surface tension associated with the water droplet.

However, it does not require much energy for water vapour to precipitate onto a particle of dust on its way to becoming a larger rain drop. Similarly, it takes enormous energy to form a microscopic ice crystal from pure water, but much less energy for water to freeze onto an existing particle of dust in the atmosphere.

The aerosol dust particles can originate from winds blowing over land or sea and picking up particles like sand from deserts, or salt crystals from ocean spray. There are also man-made aerosols that originate from things like soot and other emissions like exhaust or airplane contrails.

If there was no dust or aerosols in the atmosphere to facilitate this process, then the planet would likely make up for the lack of precipitation with an increase in humidity.