Skiing in Morocco
The answer is "yes, it does snow in Africa". In fact there are even a few small ski resorts in Morocco, courtesy of the Atlas Mountains. Tunisia and Algeria last got snow-laden in 2005 during a particularly cold winter. Snow even fell in the Sahara desert in 1979, but it lasted just half an hour.
Snow-Capped Mountains on the Equator
Heading further south, snow does fall (on higher elevations), even close to the equator. Regular snow fall has created ice-capped peaks (although most are fast disappearing) on Kenya's Mount Kenya, Tanzania's Mount Kilimanjaro; Uganda's Rwenzori Mountains, and Ethiopia's Semien Mountains. But it's not enough to ski. For that, you have to head all the way south.
South African Snowmen
South Africans can actually build snowmen somewhat regularly during the winter months (June - August) especially those living in the inland regions of the Eastern and Northern Cape provinces. Sutherland is considered to be the coldest town in South Africa with temperatures going well below freezing throughout the winter. There was a ski resort in the Drakensberg mountains, called Tiffindell but a snow maker was essential to make it through the season. Mismanagement closed up shop in May 2011, stay tuned in case it reopens. Despite its wonderful penguin population, it very rarely snows in Cape Town.
And the coldest country in Africa? The tiny kingdom of Lesotho. It's in the mountains and it has the highest low point of any country in the world (wrap your mind around that one, son). There are a few pistes and the skiing is pretty good in the Maluti Mountains. The ski season here goes from June - September.