Statistically, Memphis receives an average of 3 inches of snow per year. This amount is spread out over the duration of the winter and may include several different snowfalls.
The average snowfall in January is 2 inches and the average snowfall in February is 1 inch, while there is so little snow that there is no average snowfall in the other 10 months.
Many longtime residents of Memphis maintain that the city used to receive more snow than it does today. Theories to explain why that would occur include global warming, the idea that the bluffs of the Mississippi River deflect the snow, and the "Pyramid theory" which suggests that the Bass Pro Pyramid deflects snow storms coming in from the west. The latter remains unproven and is highly unlikely.
The two biggest snowfalls in Memphis history actually occurred decades ago, giving some credence to the notion that the city used to see more snow. The first of these snowfalls occurred between March 16 and 17, 1892 and deposited a full 18 inches of snow on the ground. The second occurred on March 22, 1968 when the city ended up with an impressive 16.5 inches of snow.
While Memphis may not receive anywhere near the national average snowfall (which is 25 inches per year), it's more likely that the city will experience several days with winter precipitation such as ice, sleet, and freezing rain every year. You can certainly expect some winter weather and icy cold days several times during the year.
In 1994, Memphis was struck by a major ice storm that caused major damage to trees and power lines, leaving more than 300,000 people without electricity for days and, in some case, weeks.