Backyard Aquaponics
A place to discuss aquaponics

I don't think you really want to use misters with Aquaponic water. They will clog.

Look into ways to flood and drain or just gently pumping water into/through the trays every hour or so.

Perhaps a system where you have a fish tank that overflows (look up CHIFT PIST systems for info here) into a grow bed filled with gravel. The grow bed would be you filter, add some composting worms into there to help deal with the solids, and the water could then drain into a sump tank of some sort. I would make the sump tank extra large so you can add an extra pump in there to water your fodder trays on a separate schedule from the growbed/fish tank pump. The added benefit is the grow bed can grow some other veggies for you, your family, the chickens and the horses.

Perhaps set up a BSF bin next to the fish tank and you might be able to call that an automatic fish feeder during the warmer months.