Is the banana a tree?
No: the banana is the world’s largest perennial herb. The pseudo-stem is formed by the petioles or stalks of the leaves. These may dry out and give the pseudo-stem a somewhat woody aspect but it’s still not a real stem.
Usually, if a banana were cut down to the ground, it would sprout up again from the roots.
Some banana species are frost tolerant and can be grown outside the tropics or subtropics, usually with some winter protection.