Apart from height and weight, older riders like me will have difficulty sitting astride a wider horse like a cob or one that has a broad flat back. My first lesson horse whom I loved dearly fell into this category.
But at that point I didnt know how to test it.
You test suitable width by looking at the position of the rider's knees aganst the saddle in halt. They should mirror each other.
If a horse is too wide for the rider, the rider will sit on the horse crooked. One knee will be further forward. I explain to student staff that an elderly person can take a long stride forward and back, but it is harder to spread ones legs open side to side.
• Weight (roughly 10%-20% of the horse's bodyweight depending on how they're built, and the type of work)
• Height (more personal preference but imo you can tell if you're too tall when it feels like there's no neck in front of you)
• Saddle fit (seen sbloom talk about this in the past. You may not be too heavy for a native pony but it can be difficult to fit a saddle if you're 'big' for it otherwise)
A lot depends on the horse though - is it a short-backed native which rides like a horse, is it a draft with a long back and wide barrel, etc
People always talk about weight but when I was looking at 5.2 and 8 stone I did not want too tall a horse otherwise day to day handling would be difficult putting rugs and tack on is easier for me with my 13.3 pony than it would be with a 16 horse. I also like to be able to get on and off from the ground in case of emergencies.