I don't have any bespoke bushy axes. My splitting axe sits by my splitting stump in all the weather the west highlands can throw at it. The splitting axe has no rust and is on it's way to out living it's third splitting stump, thats in 22 years, it has a plastic handle but the head is traditional (wide splitting wedge style) and is still remarkably clean.
I've a long hatchet/small axe, lost at the moment assumed stolen or borrowed, that I've had almost as long and it usually sits stuck in the stump. It's stayed remarkably clean too. This has a hickory handle that I periodically treat with raw linseed oil when ever we have a prolonged period of dry weather, I always oil the head too, not really necessary as the act of splitting in normal use keeps things clean enough for me.