The only one I now still open in Dubai is the one in Festival City (behind festival city).
It's taken care by Rage Shops, so I assume it's the reason why it's still on.
See the link :
http://www.rage-shop.com/site/skatepark/
I think the easiest would be for you to go first to the shop in Festival City, and they will explain you how to go.
Might be good to call them before, ensuring that opening hours (the park is only open under supervision).
I came to the conclusion that authorities didn't want any open skate park here....