I'm A Banana
Potassium-Rich
It's not a clear dividing line - the only think stopping you from having horse proficiency is that Animal Handling is more broadly useful and the distinction is often unimportant (is it key in your game to separate out people who are good with horses from people who are good with bunny rabbits? If so, maybe tool proficiency with an animal works A-OK). I think philosophically, Animal Handling is what it is because you don't need a tool to do it. Persuasion is the same philosophy - you don't have "proficiency in Fred," or "proficiency in Orcs," you have proficiency to persuade people, even though you need people to be in the room with you if you want to persuade them.You can't handle a horse without a horse. Isn't that the same issue with the vehicle or do we not count the horse as a tool because it's alive? What if the horse was a robot?
Is there really much of a difference between a skill and tool proficiency? I think every mechanic that applies to skills also applies to tool proficiency too. do we need a clear dividing line?
Skills & tools are an area of the game that is very comfortable with extensive house rules (it's all just about what ability checks you want someone to be able to say they are "good at" in the end). You could have "Fred Proficiency" or "Orc proficiency" if that distinction is important.
The main thing to keep in mind is that by RAW, you can train on a tool using downtime, but you can't train on a skill - skills are intended to be a little more character-defining, because they are intrinsic to your character's abilities, not reliant on outside objects. But it's not like it breaks the game if you change or muddy that distinction.