There are few strategies that I have used to work on my anxiousness in riding horses other than my own. 1.) My trainer will have me take lessons with one of her horses that has a different feel, personality, and training level than my horse. 2.) Now and then I will ride the horses of a couple of friends at the board where I board. These horses are different breeds and sizes from my own horse. I ride them in one of the arenas where I feel more secure. My friends are present to provide suggestions if needed. 3.) I also trail ride and/or take lessons at stables in various locations when we are on vacation. 4.) Occasionally, I will stay at a guest ranch with one of my friends where we are assigned a ranch horse for the week. Two of my favorite locations are Heart 6 Ranch in Wyoming and White Stallion in Arizona. These different riding experiences have helped me become comfortable riding other horses, but I still like riding my own the best!
I think the scariest thing about riding different horses is feeling unprepared for their quirks, and also being afraid these quirks will reveal weaknesses in our own knowledge and skills. After riding mainly my own horse when I was younger, I recently started taking lessons again - in about 2-3 months, I've probably worked out on 5 different horses, and it's been great in terms of making me aware of what I need to improve on as a rider, and how my habits affect each horse I ride. It helps to have someone there who knows the horse, of course, so you don't confuse the horse's quirks for something you're doing incorrectly, but it's really a great educational experience. I'd recommend going to take a few lessons at a barn with a varied group of lesson horses - you'll be surprised what you learn about yourself!
Try to think of what you can learn or work on with each horse you have the opportunity to ride. For example, maybe one horse is trained to a higher level than your horse. You'll be able to try out skills that your horse doesn't have yet, and that will equip you to work with him on those skills later. Or if there's something your horse does really well, but your loaner horse has trouble with, think of it as a way to improve your abilities on something you would otherwise take for granted. Think of each ride on a different horse in terms of how it will make you a better rider for your own horse. In that sense, riding other horses is more like an extension of the training routine you have with your horse.
It is definitely nerve-wracking, but it's also the best way to improve your riding. I honestly feel like 75% of a rider's skill is based on having ridden different types of horses and learning to improve each type. Then when you get back on your familiar horse, you have new tools in your riding toolbox to make him even better.
Sometimes, it is not 'fear' so much as common sense. Sometimes it depends on what 'type' of horse you're being asked to ride (is it your friend's greenie that has only been ridden twice, or is it your trainer's upper level dressage horse?) Always put safety first; wear a helmet, use your own saddle if possible, and ride in a round pen or arena, at least until you are comfortable on the horse. Ask about any quirks or habits before you mount up. And if the situation feels unsafe or out-of-control, chances are it is not worth the potential of getting hurt.
I suggest getting to know the new horse first by doing some meaningful ground work. Then ride the horse in a controlled environment before venturing out.
Like choosing a new saddle, a new horse or your spouse- this is very personal. What is comfortable for you may not be for another and vice versa. We ALL love and strive for that old shoe feeling; the one you compare every other to. We all have been there, some still are. It's okay. You seem to desire to grow your level of comfort and with that, so will your knowledge grow. Possibly by leaps and bounds ! How exciting for you! The first step is to make a decision, then commit. Soon, your actions should follow. Someone once said that insanity is doing the same thing over and over while expecting different results. I would suggest riding a friend's horse who is less than yours. Less, spirited, less active, less likely to put a hoof forward without you having to do some creative encouragement. You need to feel in complete control of every aspect of the ride. When this becomes boring, ask to sit on a horse that is as close to your own horses training, personality etc. Not much taller, nor not much smaller either. In other words, if you're used to a 16h. horse, a 14h stride can feel a bit unsettling as can a 17.3h stride. Remain comfortable in compatibility while trying different horses. In no time, your confidence in your own abilities will grow and you'll soon find yourself WANTING to try that new horse who just arrived at the barn. So, are you ready ? Set? GO !!!!! Good Luck !
Riding a new horse when you're used to one can definitely be nerve racking, but it's great that you're trying to over-come that. A good way to start is to talk to your trainer. They may be able to help you find the confidence you need. If you're up to it, you could even ask to ride a safe and reliable horse in a lesson (instead of your own). And if you get the opportunity to ride a different horse, give it a go! Even if you get on and feel uneasy, focus on your riding. If you can get through a ride with a little confidence, then maybe you can slowly step out of your comfort zone and start riding more!