the snowball fight is level 8 in the western arctic. (there is also one on level 52.) for level 8, open the treasure chest which gives you 1500 gold. you only need 1000 to build a market here, but you must clear the snowpile from the build site first. send two guys into the forestry and have the other two clean the piles of snow and fix and upgrade the buildings with the wood you are producing. take your two guys from the forestry once the houses are upgraded and spend your money on food. hire new workers at the castle until you have 10 then send everyone over to build the snow fort. once it is done the timer will stop and you begin the snowball fight. it should be quite easy to get three stars.
you have to win 2 of 3 rounds to pass the level, but you have to win 2 rounds together without losing one to get this achievement. you have to click on the blue guys as soon as they pop up their heads. be quick as they will duck back down as soon as they throw a snowball. i found this a bit tricky to do with a mouse, so if you have a touchscreen or tablet that might help out. round 2 seems to be designed to be the hardest. i've never lost round 1 or 3. something that also might help is when no one is popping up just try clicking guys that haven't popped up recently. it doesn't seem like the same guy ever comes up twice in a row and if you click a spot just before someone appears you should still hit him. for the ones who throw and duck again really fast, that seems like the only way i could get them. it's a combination of skill and luck. just keep trying. the actual level doesn't take long at all.
if you have trouble, try waiting until level 52. i got this achievement my first time thru on this one. i gave up after trying the level 8 fight about 5-10 times, but i may have just gotten lucky here. the level itself is a bit tougher, but by this point you should be able to figure out the strategy for building what you need to get the fight going.