I would say...
You can go for a ride on a horse, motorcycle, bicycle, skateboard or scooter, boat, bus, plane or ship.
You can go for a ride in a car, van, truck, tank, submarine or helicopter.
Using ride as a verb, of the modes of transport mentioned you can only ride a horse, bicycle, motorcycle, skateboard or scooter.
If someone said they were going riding, then in the absence of any other information I'd think of horse riding.
If someone said they were going for a ride I'd be more likely to assume bicycle or motorcycle, but it could also be a horse.
It's interesting that this is so complex - it's obviously one of those rule sets native speakers take on board without ever thinking about it. I imagine the OP's confusion is similar to that I felt when someone told me that in Welsh, you "sing" (canu) some musical instruments, rather than "play" (chwarae) them.