The most common conversion used is that 10 inches of snow will melt to one inch of water. That is a very rough approximation, however. The density of snow on the ground depends on many factors.
The conditions of temperature and humidity in the cloud determine the type of snow crystals that form. At close to 5 degrees F, beautiful, starlike crystals form. These crystals, called "dendrites" because they have many delicate branches, make the fluffiest snow.
When stellar crystals fall in windless conditions, five inches of snow may fall with a water content of only 0.1 inch. It is indeed possible to sweep five inches of this kind of snow from the sidewalk. At higher or lower temperatures than 5 degrees F, other kinds of crystals form--for example, hexagonal plates, columns, needles, or bullets. These crystals tend to pack more tightly when they reach the ground, thus leading to denser snow.
Quite often, supercooled water--tiny liquid droplets at temperatures below 32 degrees F--exists in the cloud where the snow crystals form. As the crystals fall relative to the droplets, they collect the droplets, which immediately freeze upon contact in a process called "riming."
In clouds rich in supercooled droplets, crystals may become so heavily rimed that they are hard to recognize. They can even grow into rounded balls of soft, white ice called "graupel" that bounce off windshields or pavement. Rimed crystals and graupel are denser than unrimed crystals.
Snow that partially melts on its way to the ground can lead to a very dense snowpack. When the snow is slushy, just four inches of it can melt to one inch of water.
Wind at the ground causes blowing and drifting snow. Snow crystals or snowflakes (consisting of many crystals stuck together) that may have arrived intact at the ground are quickly ground into tiny fragments. Drifted snow is dense. Sometimes you can walk on it without sinking in very far.
After snow is on the ground for a while, it tends to settle, even without melting. The weight of the overlying snow tends to compress the snow at the bottom of the snowpack and, because of the movement of water vapor within the snowpack, the sharp edges of crystals in freshly fallen snow eventually become more rounded. An exception occurs if there are large temperature gradients within the snow, but we won't go into that here.
In summary, 0.1 inch of water can yield as little as 0.4 inch of snow or as much as five inches of snow under extreme conditions. More commonly, 0.1 inch of water yields from 0.6 to 1.1 inches of snow.
If you want to know the density of snow that falls in your back yard, collect snow as it falls in a cylindrical tube that is preferably at least a few inches in diameter. Place the tube away from trees or buildings. Later, measure the snow depth with a ruler in several exposed places, and take an average. Then melt the snow in the tube and measure the depth of the water. That will give you the actual ratio of snow depth to water-equivalent depth for a particular storm. The ratio will vary from storm to storm.
For further reading, I recommend The Snow Booklet by Nolan J. Doesken and Arthur Judson. Published in 1996 by Colorado State University, it is a handy, 86-page guide to the science, climatology, and measurement of snow in the United States.
Weather Queries are answered by NOAA meteorologist Thomas Schlatter.