It was small, black with a light colored belly and a very bright yellow ring right behind the head. I think it was a ring neck hatchling, but I dont know much about snakes.
Ringnecked snakes are very small. I doubt it was a hatchling, as they would only be a couple of inches long and you probably wouldn't have seen it. Adults in your area aren't more than 12 inches long and slenderer than a pencil.
I have a small burro (golf ball size hole)of some sort going down under the hen house, could there be a snake living there?
Possible, hen houses are favorite hang outs of certain snakes (ratsnakes in particular).
Will it stay around the area? I'm hoping he will as he was very pretty, and I'm sure would keep the mouse pop. down.
Assuming you mean the ringneck, yes, he might. As long as their is cover (leaf litter, rocks, logs, holes in ground) and water and food (skinks, salamanders, small snakes). Ringnecked snakes are reasonably common in residential areas of the east.
As for keeping the mouse population down, no eastern ringneck snakes could even eat a newborn mouse, so it isn't likely to influence mouse populations.
I live on a heavily wooded 7 1/2 acres, so I get adult black snakes all the time.
They will keep the mouse population down (or the egg population in your chicken house if they can get it!).
Is it true that when you have black snakes, garters and other "harmless" snakes around, you will likely not have venemous species around?
No. Not true. In reality, the fact that you have non-venomous snakes around means you have adequate food and shelter for snakes. Venomous snakes have basically the same needs. Not something you should worry about on 7.5 acres. Don't pile wood (etc) next to your house and watch what you are doing when you are outside and you will be fine.
Learn to identify the snakes you have in your area and you will be doubly safe. And then you can appreciate the fact that you can share your land with these magnificent creatures!
-----
Chris Harrison