Out of interest, why do you think he would have called it a warbow? When you consider that a "warbow" was a military-issued rocket launcher designed to send massive arrows a long way, what use is that in a forest?
I always saw Robin Hood as a sneaky, silent, quick and deadly ambush hunter. Primarily hunting animals, occasionally getting into scrapes with lightly armoured patrol units/rangers.
There was a fairly poorly made BBC show about Robin Hood released a couple of years ago. I'm sure you can get it online somewhere, but it shows Robin Hood (played by Jonas Armstrong) using a lovely little Asiatic style recurve. Here's a pic or two
That looks right to me. And it being the latest (as far as I'm aware) production of Robin Hood, I would imagine all the latest research has been used for it.
P.S. You guys need to actually come to England before saying it's very wet. We get some rain, yes. So does the rest of the world. It's a bit of a myth that we live in a constant state of being underwater