What Should Happen
The /execute on owner subcommand should select the owner of a horse, donkey, llama, or mule.
Steps to Reproduce
Spawn in and tame a horse
Keep riding the horse
Run the command
/execute on vehicle on owner run say I own this horseThe chat will not display anything
Note that this behaviour shouldn't be expected from camels, skeleton horses, nor zombie horses. Those don't have the owner tag that the others do
Horses don't have owners, that is for pet mobs. To select the player that is riding it, you'd want to use
/execute on vehicle on passengers run say I own this horse