Definitely hydroids, getting rid of them can be tricky, but they can't kill adult seahorses. They can definitely be a problem in seahorse fry tank, and as I understand this is the primary reason that fry tanks are started with just water and not kept running in between runs. They will grow and be present in some form in any tank with a lot of particulate food or copepods, especially in high flow areas, and the hydra stage you're seeing here is more indiciative of their presence than actually the cause in itself - these ones probably can't sting much of anything yet.
As far as I've seen, there's not a lot you can do in particular for reducing their numbers safely, but some amount of manual removal at least in theory can help. Cleaning your plumbing and removable bits can be helpful, as they will often colonize inside of overflows, pipes, etc., but it's not like the colonies in there will be able to hurt your livestock.