Each level would make your horse swim for a longer amount of time. After that time is up, your horse would start sinking and you'd have to eject.
Level I- 1 minute
Level II- 3 minutes
Level III- 5 minutes
If having the effect last that long seems unnecessary, I'd be willing to change it.
Suggested by EnderCreeper168
The time limit for all levels of Depth Strider is three minutes, and each level up reduces the amount water slows you by 1/3. Level 3 will make your horse swim as fast as it runs on land, and any level beyond that will have no effect on speed. The increased speed of each level would allow you to go further within the three-minute time limit.
There might also be a thirty-second cooldown after the three minute time limit that can be skipped if you feed your horse.
If you have an idea, please feel free to post it. All suggestions are welcome,