When does the Yeti Zombie appear in Plants vs Zombies?

I am yet to see the Yeti Zombie in Plants vs Zombies (PC/iPhone) and I've been playing for 50hrs+.

Is there a specific condition that needs to be filled for him to show, a way to trigger his arrival or is it completely random?

Solution 1:

You need to have completed the adventure mode once. And then in level 4-10 it will appear. If you kill it, then it will randomly appear throughout the game. (source)

Solution 2:

You play to the end, then when you get to the bit when Crazy Dave chooses the seeds for you, in the fog bit where it is all black, and you can only see when the lightning strikes, the Yeti Zombie comes on there.