One of my friend's was named after her parents' cat, because it was the only name they could agree on. She thought it was a cute story, even in her grumpy teens. Winter is lovely though, and more uncommon (506th) than Willow (96th).
I agree with others who've said to choose a name that isn't a regular noun for the middle name. Especially if the last name is Green/Walker/King/Hall/Hill or any of those other top-thirty noun names. Though if it actually is Winter Smith, she might like this book :)