The majority of side-saddles are between 50 and 80 years old. This raises a series of problems; wear and tear, condition of the inside - the tree - the confirmation of the horse for which the saddle was made, and the confirmation of the rider - again, for which the saddle was made, as most saddles were tailor made for individuals.
Most horses are a different shape from those from the early to mid-1900's - nowadays, horses carry more condition. This makes the fitting of side-saddles over the withers much more difficult, and, unless care is taken, pinching, especially on the off-side wither. Fit should be snug but not tight.
The seat of the saddle should be flat - front to back, without it being raised at the withers. Without a rider, from side to side, the saddle should be raised slightly on the near side, to allow for the rider's weight when mounted, giving support to the rider's left hip, becoming level when the rider is in position.
The saddle should be of the correct size for the horse. This brings into consideration the length of the horse's back and the length of the rider's thigh. A saddle which is too short for the rider is uncomfortable, and give the impression of falling off the back all the time. If the saddle is too long for the horse, painful and undue pressure is put on the loins and kidneys.
It is a good practice to question your instructor on how to put a saddle on and where and how it should fit..
What type of horse is suitable? The simple answer is - most. Technically, few horses object to a correctly fitting, properly maintained side-saddle and sympathetic and straight rider. There are, however exceptions. In the years I have been working with horses and side-saddle, I have only come across one who objected strongly - and that was due to internal problems, he had an incomplete liver and overworked kidneys.
Conformation wise, the ideal side-saddle horse has well defined wither, with good sloping shoulders, giving the horse the ability to move straight with long, flowing strides - nothing is more uncomfortable than an upright shoulder which results in a choppy gaited horse. Ideally, the horse is well schooled, and is responsive to the aids, and can work at a good upper novice, lower elementary dressage level.
As with a horse for astride riding, a good walk is the starting point, a horse with a bad walk will seldom give a good, true trot, canter or jump. The trot, although a daisy-cutter (excessively long, low covering of the ground, with little knee action) is not necessary, the trot should be smooth. The canter is important, again straight and smooth. Hopefully, the horse will accept the bit, not bury it's head in the earth due to overloading it's forehand. In other words: self carriage. That is the ideal.
Practically we deal with all types and sorts. Cobs, hunters, blood thoroughbreds, all types and sorts. The biggest problem is the fitting the saddle. Cobs with no withers and very round barrels are very tricky to fit a saddle to, and even more tricky to have one keep in the correct position on the horse. But it can be done. The importance is the straightness and square-ness of the rider's position. Arab horses tend to have short backs and, if the rider has long legs, it is difficult to ensure a saddle fits both the horse and rider comfortably. I will not go into the thorny issue of star-gazing arab horses, many do not, and I know some very beautiful arab horses who carry a side-saddle well. Horses do not necessarily have to work up to a good standard in a dressage arena before they are introduced to the side-saddle. Basic, correct schooling is the foundation. I had one horse who was very strong and wilful astride, but under the side-saddle, butter wouldn't melt in her mouth, she loved it.
Mare or gelding - again, there is no easy answer. Some prefer mares as they have longer backs, others say a longer back is weaker. My advice is - within reason - it is immaterial, mare or gelding, a longish or shortish back is irrelevant - PROVIDING the back is strong, with good development over the loins and quarters.
Next - the rider's position.