Seahorses really produce a lot of waste, and you'd be doing your reef a disservice to add them to your refugium anyway. If you are using your refugium for nitrate export, the last thing you want to do is add a nitrate factory to it, and thats what seahorses are. They need to eat multiple times a day, they are carnivores, and they have simple digestive systems where everything goes in one end and right back out the other. They could easily produce more waste than your refugium could take care of.
The 10" height just won't work for seahorses. I'd recommend an 18" height minimum. Seahorses are "tall" fish, and to some extent won't even fit in short tanks, since they reach anywhere from 6"-12" tall from head to tail (and if you figure in sandbed and airspace, the height gets even smaller in a tank). Factor in the fact that they are vertical swimmers, and 24" water depth is more ideal.
Like Fishymann said, 29 gallons is a good starting size for a pair of most seahorses, and 74 degrees is the max you want to go without a large water volume and/or UV sterilizer considering how difficult it is to treat a sick seahorse.
You'll probably be better off looking at pipefish, but I don't know as much about them. You would still need a larger refugium. You would also have to suppliment their feedings, as they probably won't subsist on the pods in a small fuge alone. Pipefish are almost all wild caught in the U.S. and can be difficult to convert to frozen foods, so you would have to consider that. Reef type pipefish, I believe, can handle more flow and higher temps, however I think they would also be more comfortable in a reef setting rather than a fuge full of macros... someone else could tell you for sure on that though.