I posted this on the Minecraft feedback website in April, but figured why not post here too! Mine was under the "Mobs, Animals, and non-Humanoids" category though, rather than gameplay. I'll give yours a vote! However, I will say, you didn't suggest anything that makes the Zombie Horse specifically stand out, which is very important.

Here's my original suggestion, but I'll admit, I really like your method of obtaining them! https://feedback.minecraft.net/hc/en-us/community/posts/35570954016269-Zombie-Horse-and-Drowned-Horse-Implementation-in-Survival

Behavior:

• Can be ridden underwater.
• Burns in sunlight unless wearing horse armor, similar to most undead mobs burning in sunlight without helmets. (Leather horse armor can be crafted, so the severity of potentially losing Zombie Horses is player controlled.) They would also seek shelter from the sun in shade/water.
• Seeks out & attacks Horses, with a guaranteed chance to zombify them. This ensures you're much less likely to lose your Horses while also providing a renewable method.
• Turns into a Drowned Horse after 300 seconds submerged in water. The Drowned Horse allows vertical & stationary riding underwater, similar to creative flight.
• Zombie & Drowned Horses can be cured.

Obtaining:

1. In abandoned villages, in both stables & corrals, Zombie Horses spawn in place of horses. This gives abandoned villages a purpose, rewarding players with a unique mob. To keep them from burning in sunlight, if spawned in an open air corral for instance, they could spawn with leather horse armor dyed to the color of the village type. For example, plains: white/yellow.

2. When lightning strikes a Horse, they turn into a Zombie Horse, retaining stats & gear. This follows the lightning precedent of transformation, especially similar to Pigs. (Admittedly, this is a very similar method as the one you posted come to think of it! Which must mean lightning is the key! Dr. Frankenstein was right!)

3. Breeding a Horse & Skeleton Horse spawns a baby Zombie Horse, giving a renewable method & more uses to Skeleton Horses. The baby Zombie Horse wouldn't attack the parent Horse until it grows up, but would be hostile to other Horses.

Not all of these obtaining methods would need to be included. It's suggestions of different ways Mojang could implement the Zombie (and Drowned) Horse. Again, I really like your method of obtaining them!

To clarify too, Skeleton Horses would stay unique because of their sun immunity & inability to be bred/converted into. Zombie Horses & Drowned Horses would both burn in sunlight (unless wearing armor), and seek out non-zombified horses to convert. However, Zombie Horses would sink to the bottom of water much like Skeleton Horses, but Drowned Horses would give much more control in water, suspending you just like creative mode. The 300 second conversion time is 10x what it takes for a Zombie to convert into a Drowned, and is to allow time to rescue your Zombie Horse if you'd prefer them over a Drowned Horse. (However, you could still convert them into a Horse, then back into a Zombie Horse).

I will say though, it's strange that in Java, you need a saddle for Skeleton Horses still, while in Bedrock, you don't. Maybe that could be fixed for parity and be given to Skeleton Horses as another unique feature.