It depends on what you're trying to communicate. If you speaking specifically about trees, you really would not say either since trees, leaves in particular, don't change to green. They start off green.

Leaves though don't "go" or "get", they turn or change.

They leaves turn brown in the fall. or

Maine is pretty in the fall when the leaves change.

"The tree is going/turning green" may imply there's is something wrong.

It depends on what you're trying to communicate. If you speaking specifically about trees, you really would not say either since trees, leaves in particular, don't change to green. They start off green.

Leaves though don't "go" or "get", they turn or change.

The leaves turn brown in the fall. or

Maine is pretty in the fall when the leaves change.

"The tree is going/turning green" may imply there's is something wrong.