Hmmm. Ok, well both horses and seahorses are vertebrates (have a backbone), but that's the closest they're related... so we're about as related to a seahorse as a horse is.
Horse: A vertebrate - mammal (i.e. have hair and produce milk, there are some egg-laying mammals!) - Eutheria (placental mammal i.e. give birth to live young) - Perissodactyla (odd-toed ungulate like the rhino & tapir... hooved!) - Equus (includes horses, asses, donkeys & zebra)
Seahorse: A vertebrate - Actinopterygii (in the same class as all ray-finned fishes i.e. not sharks but including your Nemo clownfish, herring, sea bass... all those yummy fish we eat!) - Synganthidae - the family which includes all seahorses and pipefish - Hippocampus = seahorse.