The Snowman bonus round rule is one of the many rules that can be applied during the Bonus Round episodes. It can be offered on any floor for any character but is more likely upon entering floors 2 or 3. The rule cannot appear at the same time as the Fireman or Baby Squid Bonus Round rules, since having multiple status effects dealt to dice at the start of each turn can be messy.
When the rule activates, the player will be inflicted with 1 Frozen at the start of each turn. This makes the highest dice turn into a 1 for most fighters, but for the Robot, it makes the first calculation always produce a 1. This can be beneficial for the Robot since it guarantees at least two dice can be rolled without causing errors.
While this rule prevents high dice values from being able to show up (you'll need 2 natural 6s to roll a 6), there is a lot of equipment around that benefits from low dice, so you can use your guaranteed 1 to your advantage.