Thanks for trying out the game - I greatly appreciate your feedback
Every time the spacebar is pressed (on keydown), the reindeer jumps - so the key to the game is to time the jumps such that the reindeer both clears the snowman, and has enough room to make another jump if necessary. As noted by lowglow, holding down the spacebar does not get you very far.
The initial vertical velocity and downward acceleration are constant, so the height and duration is not random.
On Chrome the height and duration aren't random... on FF they were mostly non-random, but here and there a jump would be significantly higher (up to the height of the screen.
I didn't play for long, but it wasn't playable in FF for that reason.