Also, I'm not sure how things work around where you are, but I'm going to assume that your riding is not that great seeing that you don't know how to pick hoofs. Around here students tack up their own horses before lessons so someone who doesn't know how to pick feet must be a begginer. The reason I'm saying this is that you are planning to trail ride on your own. You should be aware that a LOT of horses take exception to being alone on trails and need a confident, experienced rider to get them to feel safe enough not to throw fits at every blade of grass.
A lot of them never get over it even with an experienced rider. So much so that adverts often point it out if the horse is capable of going out on their own. Please take note of this when judging you ability to own and ride a horse on your own. It really is one thing to own a horse at a livery and take lessons and completely different owning and riding on trails on your own. Especially for oldish novice riders like me and you. Best of luck.
I think it's completely
realistic to expect a horse to go out on it's own on the trails! I did that with my first horse and my second and my third, etc. The only horses I had that wouldn't
ride out alone was a pair of horses I bought together. They were so buddy sour that they would rear and have fits if you tried to ride them away from their buddy. I chalked that up to a learning experience........I sold those horses at a loss and learned an important lesson about trying horses out alone BEFORE you buy them. But really, if a horse won't ride out alone, they are not well trained as they aren't listening to their rider. They are getting their confidence from the other horses. Maybe that works for some folks if they have no desire to go out alone anyway, but for me that's a deal breaker. I won't buy a horse that won't ride by himself.
But other than that one bad purchase, every horse I have ever owned is expected to ride out alone and does it quite well. You just have to be very careful to buy the right horse. But don't settle for a horse that will only go out with another horse, what fun is that? What if you have no one to ride with that day? Gee, I can't go riding because my horse won't go out alone?
I would venture to guess the majority of horses sold as trail horses will ride alone. My very first horse was an Arabian and I was as green as grass (I never had a single lesson, my only experience was riding rental string horses) and we both rode out alone from basically day one. Not to say there wasn't a learning curve. It look me about a year to really feel comfortable with my first horse. But we still rode out alone.
I don't know if you necessarily have to buy the horse before you move and then bring it with you. There are plenty of horses and horsemen in Arizona. So I would just go with whatever works out best for you.
By the way, gaited horses and mules are very popular with our local trail riders. Most are retirees. I am a bit younger but I still love the gaited horses. And a couple of our riders also have lovely mules. Both are a good choice. But I wouldn't even limit yourself to either a gaited horse or a mule. That might be your ideal choice going in, but you might find the perfect horse for you that is another breed. So keep an open mind.
I don't know what kind of riding you would like to do, but for me, I mostly walk out on the trail and enjoy the scenery. I ride for relaxation and to see the wildlife. So even though I might trot or gait a bit, 95% of my ride is at a walk. So you wouldn't necessarily have to have a gaited horse to enjoy the trails unless you really plan on doing a lot of gaiting. And even then, depending on where you live, a lot of the terrain might keep you walking more than any other speed.
Just some food for thought. Best of luck!