This is a much harder fight for the Survival Hunter than both marksman and BM (Beastial Wrath and silence shot help a ton). With proper patience and quick fingers you will be able to really make the mage have a bad day. Let's explore some aspect of this fight.
1) Do NOT let them get any shatter combo's on you. If you are unaware of what this means, let me tell you. If you are frozen in place you are at risk of taking burst damage. When frozen in place I immediately trinket and break the freeze. The shatter combo has a mana to damage ratio better than probably anything else a mage can do. So, if you are frozen in place do everything you can to get free. Feign death, scatter shot the mage (and don't hit him, let the scatter last the full duration), trinket out or sleep the mage. Just try to focus on not letting them get extremely (mana) cheap burst damage on you.
2) Mage + Healer - If they call their elemental then you no longer see the mage. The mage is dead to you until that pet is gone. The pet is too easy to dispatch for you to take his 800 damage water bolts. Three shots and hes gone. Mage + DPS - This is where you have a crucial decision. If you feel you won't live very long then you may want to try and burst the mage and ignore the pet. If you are well geared and can afford to kill the pet (this usually means you have a healer teammate). For me personally, I 95% of the time drop the pet. If I crit, it usually only takes 2 shots.
3) Which sting? Make it a rule of thumb to always use Viper Sting. Frost mages are great at mana management in PVE, but for arena they use very costly spells all in rapid succession (assuming you aren't letting them get shatter combinations on you). Two sting and their constant drain and they will quickly ice block or sheep you to get their mana back.If they have a healer, it is still phenomenal to drain their mana. Without mana, the healer + clothie combination without offense will fail miserably. So, either way the mana drain is best. Besides, serpent sting is not enough to help with burst anyway.
4) Your pet!? First and foremost she belongs on the healer. If there is no healer, then it is kind of up to you. If you are trying to take the mage down first then might want to toss the pet on the mage early to help with overall damage dealt. Mage versus hunter seems like it should favor the mage. Most good mages will make you feel like it does. Just know that shatters are what they will kill you with. If you are frozen in place, then do everything you can to get free or stop the mage from casting. Good mages will run right up to hunters and you should take the opportunity to wing clip and drop a trap.
Traps are your decision. Snakes are great for mind numbing and freezing is great for recovering from a flurry of ice damage. Also, when a mage gets in your face, a good strong raptor strike may get them to retreat. Whatever you do, keep the damage going. Don't turn your back and try to run, odds are if they are close to you, then you need to start thinking "How will I beat this mage in close quarters" instead of trying to get away. At least do something while you await a cooldown.
In the end, the fight belongs to the player who makes the best and quickest decisions. If the mage uses their pet and gets two shatters on you early, odds are they will win. If you can keep them ranged and keep using your crowd control on them, then you can occasionally win the fight without being touched. Be patient and aware and I promise you can frustrate even the best mage. I have watched a mage try to frost bolt me once (feign death), twice (scatter shot), three times (wyvern sting) and even on a rare occasion a fourth time...all while I am frozen in place.
Beware of mages in freezing traps! Clever mages will ice block while trapped and foil your plans for a big aimed shot. When an ice mage ice blocks, I simply pull my pet to me and feign death and then shadowmeld. Any character can abuse the mages ice block, simply bandage immediately no matter what health you have. odds are they will break the block early to stop you or you will simply gain X amount of health back!
Note: This is a unfriendly Survival hunter fight. You hit harder but if they can stay in close quarters they will beat you without taking much damage. if your having trouble then open with Viper sting, at least their mana will be gone shortly after you die! (good rule for battlegrounds)
BM short tips: Use the wrath and do everything in your power to kill them during this time. Luckily you can save your trinket and such for after the big red fades. I would suggest a wing clip and an intimidate to maintain line of site for your 18 second rampage. Also, mana drain them as well. They wont be able to kill you in those 18s, so make sure that when the 18s is over they have spent cooldowns and wasted a lot of mana.
Marks short tips: Marks has a great defense for the frost mage. As stated above, you can truly stop many casts. For you marks fellas, you have the ability to stop a shatter combo simply by doing 1 silence shot and as soon as the silence ends you can scatter trap them. Every time they freeze you in place you should silence shot them. If they get you faster than the cooldown then its time to burn the trinket. Also, save rapid fire for the moment the pet drops if at all possible. This will make you drop the pet and still get a scatter shot + aimed shot combo on those pesky mages who live for days.
Subtle reminder : Rain the arcane!!
Happy mage hunting!