I am in Michigan and I hardwired a long 12 gauge cord with a plug on the end to the house. When I need power, like in the winter, I simply plug it into the outside GFCI outlet. this was my way of getting around the code regs. My building/coup sits on blocks so it is not considered permanent and having the long cord like that makes it more like plugging in an outside appliance. I don't think there is much the county code enforcement can say about that. As far as your situation, if you are going to bury the wire I think you will find code says it must be in conduit from the building(s) into the ground, then from point to point underground it does not have to be in conduit but must be approved underground cable. I think the reason for the conduit from the building into the ground is to avoid things like weed whips from cutting into the cable. Your cable needs to be buried more than 6" though. I don't have my code book in front of me (and it is old anyway), but I do believe you have to bury it at least 18", I would consider 24" even better. If I wanted to find this out without asking too many questions I would call the county and get a copy of their pool installation instructions where it should tell you how to bury the electrical for a pool. The same would apply to your coup. Also if you are going to bury the wire make sure you know what services are already going through that area, like other electrical lines, gas, telephone, cable tv. If you cut through one of these it could cost you a lot of money. In Michigan we are suppose to call "Miss DIG" and all applicable services come out and mark where their lines are in your yard. Maybe after reading all of this you no understand why many of us chose not to bury the line. Also, I rather doubt your chickens need the additional heat in the winter. I think many people do it for their own peace of mind, but necessary it is not. Do a little searching here and then make up your mind. there are still reasons to have electric in the coup, like for warmers to keep the water liquid in the winter and lights to see what you are doing when you close up at night.
I hope this helps!