What did the woolly mammoths eat during ice age?

I doubt it would be able to find anything to eat during the winter of the ice age. That's why they are fat during winter. I think during the summer the mammoths had a wide area of food so they ate while they can. It's a bit like a squirrel before hibernation. It eats all it can get it's hand on before autumn is finish.

And being fat during winter helps with heat loss. So they don't freeze to death.