I couldn't believe it either when I heard it! However, a peek at Snopes.com and a BBC article reassured me that it does exist. You can visit Ski Dubai's website for more information, including a .pdf on how the snow is made.
Ski Dubai has real snow. Snow is made using a simple procedure similar to how snow is made at outdoor ski resorts. Pure water, with no chemicals added, is put through a chiller to cool. It is then sent through pipes to the snow guns which are on the ceiling. When the cooled water is blown out into a freezing cold environment, it crystallises and makes snow. The final product is real snow, as if it came from nature. We just give it a little help.
Yeah, and another thing that helps keep the snow around are the kilometers of tubing that run under the snow base to chill it. (Think: the tubes on the back of your refrigerator.) The place manufactures 30 tons of snow daily. Year round. Whoa.