From reading prior threads, I've concluded there is no perfect answer. Many people keep the feeder/waterer inside and many people keep it outside. I think there are many factors in the decision. Since you don't have a lot of severe weather and you have a small coop I think it would be reasonable to have them outside if you can keep the rodents and ants out of it. Hanging it would keep the ants out but it with take effort to make the coop run rodent proof. There is a "trigger-feeder" sold on e-bay by Kate & John McCullough from the UK. There is a video of it on You tube. There are positive comments about it on this website. I bought one but haven't used it yet. I will get my first chickens next month. There are treadle feeders out there, but they are expensive and I think fire ants would be a problem, since they sit on the ground. Do you have fire ants in Oklahoma?
Keeping the waterer inside has benefits of; less algae and easier to keep water from freezing in the winter. Some people who use nipples complain about leaking which is more of a problem inside the coop. I think the waterer will be more cumbersome to change out inside a small coop. I also have a small coop in Texas. I'm going to use a thermal water jug outside the coop/run with tubing that goes to the run and water cups from beaktime.com. It is insulated and I plan to put ice blocks in it in the summer and a 5 gallon bucket deicer in very cold weather. It took a bunch of adapters to get the tubing to plug into the spout opening of the water cooler and the fitting on the water cups. See pics below
Having said all that. When I get my 3 silkies next month I plan to keep them in the coop a day or 2. So I will take out the nest box and put in a small waterer and feeder inside the coop for a couple days.
this is the waterer outside the coop. I will thread the tubing through the hardware cloth and mount the cups inside the run
this is the feeder. There is a trigger fitted through a hole cut out of the bottom of the bucket you can't see in this picture. The metal cover at the top is to keep chickens from sitting on it. The hardware cloth around the bucket is to protect the thin plastic bucket (may be over-kill?).
Here you can see the "trigger" sticking out of the bottom of the feeder. The chickens are supposed to peck at this and feed drops down into the pan .
This the inside of the coup. I have a waterer hanging from the inside of door that I plan to use for a couple days. The roost bar is towards the back with "chicken stairs" in the middle to help them get to the roost bar. There is pine shavings in the bottom for bedding. The white plastic piece of board under the roost is my quasi "poop-board" since I don't have room for a real poop board. The wood planks under the nest box are a removable "kick plate" of sorts to keep the bedding in the coop.this is the whole coop/run. You can see the waterer and the feeder through the hardware cloth. There is a green composter at the right of the picture.