Pure personal preference. You’ll find some of us have feeders inside, some outside, and some in both places. The only rule is that it needs to stay dry. And even then some people purposely wet their feed. There are advantages and disadvantages to all three.
If it is inside, they will spend more time inside. Chickens poop a lot wherever they are. If they spend more time inside you might find yourself managing the poop a bit more than otherwise. Might. Depends on number of chickens, size of the coop, and how you manage the bedding and poop anyway.
Some people find if they put food outside they wind up feeding a lot of wild birds.
Some people feed outside to try to not attract mice inside the coop.
If you let your chickens out fairly soon after they wake up, it doesn’t matter. But if you like to sleep in on the weekend or they wind up locked in the coop for a long period after they wake up, it’s probably a good idea to have feed inside where they can get to it. Water works the same way.
Feeders can take up floor space. When chickens fly down from the roosts, they need a certain amount of clear floor space to land. Hopefully your coop won’t be so small that this becomes an issue but I’ll mention it anyway. Also, the feeder and waterer need to be positioned so the chickens cannot poop in it from the roosts. Is your coop big enough to accommodate this?
What is your climate like? Will the chickens be able to get outside to eat in all weather? This somewhat depends on how you build your run to keep snow out if snow is a consideration.
If you integrate other chickens, it makes integration go easier if they have separate feeding and watering locations. It avoids conflict.
I’m sure I’m missing several things, but we each have unique situations and different goals. Like practically everything else concerning chickens, it’s not so much a right way or wrong way, just which way better fits your situation.
