I have lots of suggestions...need more info on the type you want to use and how many goats your feeding. Do you want something attached to the wall or a free-standing type?
As for keeping it outside that is fine. I live in an area that gets alot of snow so I have a cover over mine to keep the hay from getting wet. I also have one inside because when it is nasty cold out they don't venture out much...so you'll have to evaluate your weather and how you want to do it.
2 legged kids: Tyler, Ethan and Kyle Does: Lucy, Nancy, Katy, Daisy, Annie, Dotty, Kelli, Kayli, Sally and Nana Bucks: Mr Big, Albert, Ringo and Charlie Brown 16 Horses (QH and Paints) 32 Cows (Hereford X) 6 Hogs 72 Chickens (Isa Brown...egg laying fools)
I made a freestanding hay feeder out of a cattle panel, made an 8 foot section into a circle and put a rack in the bottom of it about 12 inches from the ground, as long as the goats don't have horns thay can't get stuck, I have mine wrapped with fencing that has 1x2" squares to keep heads out of it...the whole thing stands a little more than 4 feet tall and will hold a full square bale.
What I have done inside the shed to feed hay when the weather is wet is take pieces of fencing( a 3 foot section works for mini's) and nailed it to the wall, the bottom half flush and the top puckered out enough to slide a flake of hay into. You can place it high enough so that they can't stand on their hind legs and reach down into the top.
I've also attached pieces of fencing to the outside of the pen fence and used wire to attach the bottom and the sides for outside hay feeding, place a flake between the 2 "fences" and theres an easy hay feeder. If you place a feed sack between the hay flake and the outside piece, the hay won't drop on the ground out of reach.
I've been using big buckets One in the pen and one outside. The outside one gets flipped over when the girls go in their pen for the night in case it rains. When our barn is finished I'd like something that is a more permanent fixture inside. Someone on the forum said they got a big wooden crate from an auto place and pulled out a horizontal slat around the outside of it so the goats could get their heads in, and it cut way down on wasted hay. Might try something like that...
Liz, do you happen to have any pics of your hay feeders?
These are the racks I have inside....the one has plastic trays from a commercial bread rack...I cut goat nose sized squares across the bottoms and the cattle panel holds them in place...I shoved 2 large handfuls of hay down in the bottom at 8 this morning and there was still hay there at 3...no waste either. The panel on the wall is a goat panel with smaller squares than a cattle panel...it works well too.
The other is a piece of garden fence stapled to the wall....holds a flake very well.
An outside feeder that I use on occassion is an old oven rack attached to the outside of the pens fence panel...hay sits snug and the reach through the panel squares with their noses to get it.