Are you talking regular short trips, to pony club etc, or long haul distances, one off type moving?
Regular short trips - does not work that well, whoever owns the transport is often put out, because it is a big demand on their time and resources, if it becomes a regular thing. They would have to be a saint to encourage it. I did occasionally borrow the neighbours float - but as at the time did not have a tow vehicle she had to drive me as well, so it was not a regular thing. I would pay her, but I never felt comfortable with the arrangement. Thankfully, I was able to obtain my own transport soon after.
Also just the logistics of the whole thing, being ready to leave when the other party is not, how well the horses travel together, etc
Long trips - absolutely, I use a racehorse transport company and the costs being split between a number of owners, makes it very economical.