As the saying goes, Dubai has two seasons: the warm season, and the hot season.
It really depends on what you're used to, though. I'm from The Netherlands, and the weather we have in Dubai in December and January would be similar to a nice summer day back home. Having lived here for nearly five years though, it feels chilly when it's 23C (and I'll wear a sweater).
In July and August, and to a somewhat lesser extent June and September, everybody lives indoors; it's too hot to be comfortable outside (always over 40C, often over 45C, even at night (temperature goes down a bit, to around 35C, but humidity goes up a lot to compensate...) Fortunately, everything is air conditioned (even the bus stops).
The rest of the year is great though. Do note that especially in February, it might rain, and in March, there may be dust storms.