you should really get at least a 29. Yes they do like the height. A 30XHigh is ideal. I had one for a couple of years with reidi in it. I now have a 29 reidi seahorse tank. It has worked just as well as the 30Xhigh. I find that keeping the room temperature down around 72 is pretty easy. I've never used a chiller, but if you're water temp is going to be much higher than that you may want to look into one.
I defenitly agree with Ade on the tank raised. I accidently got one once that wasn't. They almost never eat if they are wild caught. Make sure when you order is specifically says tank raised.
All in all I've found them surprising easy to keep. Don't be afraid to try it. Just do your research first. There is controversy over several things, one of which is protein skimmers. I've never used a skimmer with my seahorses because of the risk of gas bubbles disease. I've always just used a regular hang on filter, works great. If you have any questions please let me know and I'll try and help you.
Best of Luck