Yes it does depend on the horse, or on the stage it has got to in its transition. Horses who are trimmed by EPs are given a score out of 10 and each increment indicates the sort of work it can do. By doing too much too soon, the horse is likely to regress, but in keeping within the scale of usability, you can expect a transitioning horse to increase its score steadily, although it's not unusual to lose a few decimal points for example when the ground is hard or there has been a long period of wet weather. Some horses come straight out of shoes and score maybe a 7. Those are the native types that won't bat an eyelid at going barefoot. Other cripples like my girl might score a 2, but after a year obtain a 6, which is "normal". A 10 is almost non-existant!
Getting back to the question, road work is part of the barefoot transitioning process, helping stimulate growth, build concavity and correct underrun heels, but only as much as the horse is capable of at the particular point in its transition which can take years, or not, depending on the horse. A friend of mine does a lot of road work with his barefoot horse, who is ID and has good feet. Short walks on concrete or tarmac will be advised by EPs when a horse is much lower down the scale for its therapeutic benefits.
Horses who are not yet at an advanced stage of transition will happily hack on the roads in boots, which are really no major inconvenience in the scheme of things.
Agree with everything Lynwood says. Plus barefoot horses are far less likely to slip on roads than shod ones as they can use their heels and frogs effectively as brakes.
Roads are actually a good surface for a horse transitioning to barefoot/unshod/no shoes as it is a consistent firm surface. There is far less concussion on an unshod/barefoot/no shoe horse's foot than a shod horse too.
But obviously going barefoot/unshod/taking shoes off doesn't suit every horse and owner. At the end of the day it is about what is best for the horse.