Cherie - thats a great question "how can you find a new home for a clicker trained horse".
This is why my clicker trained horses are taught to respond to pressure cues. I use non-escalating pressure to cue the skill I want, c+t to reinforce it. The clicker is only used to teach the skill, not used for all eternity. When a skill has been learned you can either reduce the reinforcement or you can increase the criteria of the skill. Like asking for a more collected or extended trot rather than just a trot. I never stop training my horses, I'm always CTing for something new, but other peoppe ride my other horse and the rescues I train without using CT. The skill has been taught, the horse knows what's expected of them. My horses are taught to respond to all sorts of tack options, bits, bitless and no tack. I expect them to listen 100% of the time, food or not, the rewards are just used to teach the new skill or reinforce a skill that may be lacking.