Frost mage can be tricky if you are new to the game and blast all your cooldowns like a chimp.
This is true especially in arenas.
In the end its more of a "learn to play" issue, since Unholy DK as a whole is more than capable of soloing arenas in a 2v2 against casters.
Try reading trough: http://forum.warmane.com/showthread.php?t=316091 and finding some youtube videos for tips and tricks.
in low rating bait their blink and keep ur grip for after they blink, then theyll either frost nova or cone, or block until their blink is off cd/nova, usually theyll nova, blink and try to get a deep freeze off so keep ur ams for after u grip since thats when theyll nova+blink, but shouldnt be too much a problem