The rock itself is not "live", it's the bacteria that grow on it, making possible the biological filtration of the rock that makes the rock "live". Bacteria grow at any water temperature that any life forms live in so you don't have to worry about that aspect.
Many people, like myself, boil rock before using it to lessen any affects that might come from passing on pathogens to the seahorses from it's previous source, and then cycle it with ammonia to reproduce the bacteria. That is also the cheapest way to set up as "live" rock is more expensive than "dried out" live rock and boiling it takes care of all nasties. Pick the most porous pieces of rock for best biological function.
The present day recommendation for keeping seahorses is to maintain temperatures in the range of 68° to 74° even though the same seahorses come from warmer waters naturally. This lessens the chances of bacterial infestations very common with seahorses in aquariums where the water isn't ever changing like in their natural habitat.
I haven't kept temperate species to date but suspect their range to be a bit lower than that.
As for type of seahorse, it's best that you keep to one species even though some have had some luck with mixing. Many hobbyists who have mixed species of seahorses though experience problems where one species can't handle the pathogens introduced to it by others.
I have put my experiences on my website and can be seen at
THOUGHTS ON SEAHORSE KEEPING
At the bottom of my page I have links to what I believe to be excellent information for starting keepers in their new quest.