You don't have to kill him to complete the quest. All you have to do is open the locker.

Rogues can sap.
Warlocks can fear and send pet. (Capable of killing)
Hunters can send pet. (Also capable of killing)
Mages can sheep.
Priests, Warriors, and Paladins can QQ (Or find one of the above classes).

This was a very easy quest as Night Elf. I parked in the corner were the Copper nade spawn was to the right from the cave and simply used Shadowmeld and waited him to come out. While he ran out i runed to the chest that is to the left when u enter the cave and i ran to same corner and Shadowmelded again until he was in the cave again. But try be quick because after he have patrolled the outside he runs to the cave very quickly so do this with auto-loot or something of the other loot options.

I did this as a lev 9 warrior and after I died attacking him outside his cave, once he left it, I had plenty of time to run in and loot the chest. Dead simple to do.

As previous posts saying, at some intervals, https://vanillawowdb.com/?npc=1271 Old Icebeard leaves the cave and patrols the area. So if you are cautious, you can easily avoid confronting this yeti.
This is how https://vanillawowdb.com/?npc=1271 Old Icebeard patrols:

1. He hangs around in the cave about 5 min.
2. He walks out the cave, turns left, and stands idle shortly at the opening.
3. Then he runs back to the cave. Yes, he runs back. And so on.

Process 2 and 3 took him about 1 min. So that, you should at once retrieve the contents of stash and leave the cave within 40 sec or less otherwise you will get caught!

Hahaha, I died once before realizing I could just sheep him....

I'm a terrible mage :D

Just a funny note, but he has 666 hp.

This quest is easy to mages, warlocks and hunters. Mages can polymorph him and take the chest. Warlocks can send minion to attack + fear + curses + shadowbolt.
Hunters just send pet to att him and shoot until he's down. It's not hard for the other classes as well, but some might need a health potion.

Did it as a level 9 Night Elf Hunter.
I pulled him out of the cave with Serpent Sting,
Waited for him to come as close as Concussive Shot is limited to, fired it.
Then I ran into the cave, looted the chest, tried running out of the cave,
SHADOWMELDED (gives you a second or two for him to reset).
Fired another Concussive Shot and ran out of there.

if you don't want to fight him:

if he's in the cave, just wait on the little platform overlooking the cave entrance. he'll come outside in less than 5 mins. as soon as he starts walking out, move down to just out of aggro range on the right side of the cave. when he walks out and turns and starts walking up the valley, move quickly and you'll have enough time to get back out without being seen. thus the ""stealth"" Tundra was talking about in the quest description.

every 5 mins (while he's alive), he comes to the mouth of the cave. he turns right (your left as you face the cave from outside), and walks up the valley maybe 30 yards, then runs back into the cave. during this afternoon constitutional, you can run in and loot the chest... which is on the floor at the back of the cave. it's brown, the cave is white, you'll have no trouble spotting it.

Icebeard's hp: 666.
time needed to open the chest: 1 sec.
time Icebeard is outside the cave: 45 secs.
time between walks: 5 mins.
respawn time: 1.5 mins.

for rogues who haven't got sap yet
use gouge

if u run in and gouge him you will have just enough time to open the box and start running out