Steal one

Seems obvious, no?

If you’re asking about permanently getting a wagon instead of a horse, you cannot

Just to ride around on ? Or to keep ?

To keep but I think it's not possible

Oh okay, I agree, I don’t think it’s possible :(

Wagonjacking

You're confused

You can’t own wagons in story mode only in online. But you can steal wagons all the time. The two wheel, one horse wagons or small carriages w one horse are the fastest and don’t they don’t lose stamina.

There's a dealership just north of Rhodes.