If you go hosing down an *indoor* gravel floor, my experience with horse barns suggest that what you will get is intractable humidity for at least a couple weeks if not longer. And in cold weather that would be a VERY serious problem. I wouldn't do it, wouldn't even consider it. If you don't hose, you will need to use removeable bedding, and it will mix with the gravel and you'll eventually end up finding you've dug the floor out while you're cleaning and wasted all that gravel AND created a bathtub for wet-weather flooding.
Is the area small enough you could put big pavers (like 18x24") on the gravel? That would be a really good solution, and provide pretty decent predatorproofing too. And then obviously put a good layer of shavings on it.
JMHO, Good luck, have fun,
Pat