Yetis require a healthy diet.

They can't survive off of only rocks and meat. They need to eat plants, too! And if they do eat them they become even more fearsome.

When Nunu Consumes plants they act differently than if he had attacked them (120 second cooldown):

Honeyfruit: Restores Health and Mana only to Nunu. He can reactive Consume to gain a shield based on his maximum Health. Blast Cone: Nunu's next Ice Blast is unstable and explodes on impact, knocking nearby enemies away from his target. Scryer's Bloom: Nunu gains True Sight for a while.

Edit: Whoops! Forgot about Brambleback. Maybe its fire burns up its roots and leaves before Nunu can process them?