It is possible to swim in deep water before buying the flippers from King Zora. This is useful for quickly getting from the Desert Palace to the Tower of Hera via the whirlpool warp east of the desert.
To do this, stand on a ledge above a body of deep water. Get as close to the edge of the screen as possible and face the edge of the screen with your sword out. With sword drawn, jump into the water and immediately hold towards the edge of the screen. If done correctly, you'll change areas on the same frame you hit the water, canceling the drowning trigger and allowing you to swim normally.
It is possible to softlock the game if you get hit while swimming in deep water without flippers. This can be dangerous when using the Desert Palace to Tower of Hera shortcut due to the Zora that spawns in the water near the portal.