Where did it come from? Did you buy it? Did you get an order in recently for something else? Can you post a picture?
Seahorses typically move up and down. The slime is probably brown algae covering its body -- that's not unusual and really isn't a problem. It doesn't hurt the seahorse.
It could be a dwarf seahorse. If it's smaller than a neon goby, it's probably a dwarf seahorse. They grow up to 1 to 1.5 inches tall, from tip of the snout to tip of the tail. They are very small! If it's a dwarf, they eat LIVE baby brine shrimp ONLY, which you would have to hatch every few days. Also, dwarves are NOT safe in a reef. Just about anything in there would kill it or eat it, including many corals and inverts.
Or, it could be a very young seahorse of a larger species. Young H. Reidi are flooding the markets now, coming out of Vietnam, I think it is. They are raising them in ocean pens there in huge numbers. But usually, these are at least 3 inches tall when they arrive at an LFS, so I doubt it's a young specimen of a larger breed. If it is, it could eat frozen brine shrimp if it's a really small horse. It sounds really small. Eventually, you would want to feed it frozen mysis. However, it may not yet be trained to frozen food, so you'd have to feed it live (baby brine shrimp, brine shrimp, tiny ghost shrimps) food until it got switched over. If it's as small as you indicated, it can only eat baby brine shrimp and copepods. Seahorses do love to hunt for copepods.
Seahorses should not be in reef tanks, though. They really do need to be in a tank of their own, a tank that meets their special needs, slow flow, low light, no tankmates that would compete with them for food or threaten or stress them. They are very vulnerable.
If it is a seahorse, I suggest you take it to a reputable LFS and let them care for it.
I would have a better idea if 1) I knew where you got it, and 2) I could see a pic.