The question isn't whether a snowman will stop a JHP, but whether a JHP will stop a snowman.
In most cases it all depends on whether the snowman has been drinking or is on drugs.
I suspect any 9mm bullet would penetrate that much snow provided it wasn't packed into ice. Expansion normally only occurs if there's fibrous material combined with water. Wet phonebooks, gelatin, flesh and so forth cause the bullet to peel back and expand, but I'd think snow would not have the same effect.
Forty-five ammo usually doesn't have great penetration, which is why it's a poor hunting round, but works well on humans (works better if you stand in front of a fan...it can use all the help it can get).