Hobson's Choice is almost always used incorrectly. It is supposed to mean no choice but is almost always used to mean a difficult choice. Thus, in today's example usage - "There, many are given a legal Hobson's choice: Plead guilty and go home or ask for a lawyer and spend longer in custody." - the poor citizen does have a choice, albeit between two very different outcomes.
Does it really mean no choice? In the original situation, you still have a choice between the first horse, or not having a horse at all. This is only "no choice" if having a horse is an absolute unequivocal must. You could always walk, or wait for someone else to come and take the first horse, or go somewhere else for a horse, or ...
I think the legal example is quite accurate - you can either take the (guilty) horse, even though it's not to your liking, or the (walking) imprisonment, which might get you a better outcome but will require more time and effort. I suspect the phrase has survived
because it appies so well to these almost-but-not-absolutely no choice situations. Otherwise one would just say that one had "no choice".
