It's very much better to site the feeder under cover, as even with a rain hat, you'll find that rain will make the feed damp by blowing in sideways in windy conditions, or just by penetrating the feed if it's drizzly or misty. Feed spoils very quickly, it will clog and block the flow, and go mouldy, which is toxic to the hens, and you'll waste a lot if it's left out in the open. I did once try a feeder with a large rain hat but not only found the feed got damp, but also that the hens didn't like having to get in under the hat if it was low enough to be even partially effective. So I threw it away.
If you haven't yet got a roofed area in your run, you could perhaps make a feed shelter out of an old table or similar, with three of the sides filled in, and place this so the open side is away from the prevailing wind.