My idea for the yeti is quite similar to yours.
The yeti will behave as usual but with the additional snowball throw after before the stomping.
So the yeti will run from one side to the other, jump on the higher ground, throw two to three snowballs at the player wait a bit (maybe until all snowballs are defeated), do the stomp attack and run to the other side and so on and so forth.
In pinch mode (reached when the yeti has only two lives left) the yeti will "hop" from side to side making it harder to jump on him (idea from HybridDog on github:
https://github.com/SuperTux/supertux/is ... -485275845), then after throwing the snowballs and stomping the yeti will throw one last gigantic snowball and "hop" from one side to the other and so on and so forth after the snowball reached a wall and breaks.
The first boss should not be too complex as it is the first boss in the game therefore should retain a certain "easy" difficulty. Later boss however can get complexer.