It's one of those things where the relationship between skills and tool proficiencies is a bit "funny".
Skills are worth more, and only acquired through set character building resources (race, (sub)class, background, feat). Tool proficiencies aren't worth as much, and can be acquired through any of those means, but also just by spending downtime.
Taking a skill is a limited life defining decision, most characters won't gain any more than they have at 1st-3rd level. On the other hand, you can pick up dozens of tool proficiencies without gaining a single level.
When it gets "funny" is the few examples where the power comparisons don't exactly work right. For example, Thieves' Tools are are almost as good as a skill (some might say better than some skills).
The situation you're running across is similar the musical instrument versus singing issue. You can learn how to play a musical instrument with a tool proficiency, but the only thing that gives you proficiency in singing in the broader Perform skill...which doesn't make any sense. In a similar vein, you can learn land vehicles, water vehicles, probably air, space, astral, whatever vehicles with a tool proficiency, but you can't figure out horseback riding without taking that more general Animal Handling skill.
However, it's worth noting that tool proficiencies occupy exactly the same space as languages. This conceptually suggests that any learned trait that is of a similar level of focus as one of those could be learned in exactly the same way. If it's more like a tool or a language in breadth and power than like one of the set skills, you should probably be able to pick it up like one of those.
My personal solution is to be flexible with new "tool" proficiencies. For instance, I allow someone to take a proficiency in a specific style/genre of singing, in the same manner as they'd take a musical instrument proficiency. Perform is still broader, but you don't have to devote your life to it to pick up some singing. In like manner, I'd probably allow a "vehicle: land mount" kind of tool proficiency.
Of course, if the "tool" word is really holding you back, you could always consider creating a "Saddle" proficiency. ;-)
