Let's come up with an amphibian race!

Or should we give them seahorses instead, which would swim everywhere and be very easy to summon?

Horses will have to be abandoned. For example: you reach a body of water, leave the horse on the shore, cross the sea, and end up on an island. You need a horse again for land movement, but where do you get it? It's on the opposite shore, and you are on the island. How will it run to you? It can't exactly swim to the island. In this case, it would be foolish to leave it on the shore at all... We need something else.

Added after 1 hour 8 minutes
I guess I'll have to put amphibians on a ship for sailing across the sea surface after all. Even though I don't like it, I don't see any other way for now.