The only times I have ever beaten good (I stress good here) Frost Mages is by playing defensively. Don't just start trying to lay into him with your LB's and CL's, because if you try to turn it into a damage race he will floor you, and soundly.
The only spells of his you can Earth Shock are Frostbolt and Polymorph, which, again, if he's smart, he'll use sparingly. Do not, whatever you do, allow him to land a Polymorph especially, because then you are going to eat a big Frostbolt and then the fight is just going to start all over again with you at a disadvantage.
Most of his damage is going to come from Fire Blast and Ice Lance spam, the latter of which is really going to hurt if you're rooted. Nothing you can really do there but try to heal through it.
Counterspell is really the lynchpin in their entire operation. It shuts us down completely for what'll seem like an eternity. They're going to try to DPS you down to the point at which they think they can kill you, then Counterspell you and proceed to do so. Stick to the general rule of "heal fast, heal early", and if you're really lucky they'll burn their Counterspell early enough that you can still recover from it. Don't count on that happening with a good one though.
Don't waste Grounding Totem frivolously. Save it for times when you're rooted to absorb a big Ice Lance, times think you can get away with an LB/CL cast, or when you absolutely need to heal. If you lay a Grounding Totem right before you cast one of your big spells, the Mage has to stop whatever he's doing, deal with totem, and then try to Counterspell you. It's very, very rare that they'll be able to kill the totem and cast against you before your spell finishes.
Keep Purge on a hair trigger. Don't ever try to cast LB/CL or any other offensive spell when you can Purge their Mana Shield or Ice Barrier instead.
If he Ice Blocks, heal. If he Ice Blocks and drops the Elemental, it'll go down quickly to a lightning spell and Flame Shock. Kill it, then heal. If he drops the Elemental outside of an Ice Block, kill it anyways while trying not to eat a big spell from the Mage.
Um... I just woke up, so those are all of the tips I can think of off the top of my head.