I love writing books too and am pleased to see your book will have horses in it. Horses make everything better! : ) I thought I would just throw out some things you could think about
Firstly, I don't know anything about the characters your writing about, but they impact things greatly. Horses are very sensitive creatures and know if their rider is nervous. If a horse senses their rider is nervous, the horse can get nervous too. So If any of the characters are scared about riding the horse, the horse will know. Also, you mentioned their riding the horses through the forest? In that case the uneven ground ads an element of difficulty. Going down hill on horse back can feel quite wobbly and scary to a new rider, but their should't actually have any risk of falling as long as the horse is justing walking.
Which leads me to my next thought, the speed of the horse. Horses have four basic speeds: walk, trot, canter, and gallop. Obviously, walking is easiest. Anyone should be able to stay on a walking horse. Trotting is very bouncy though, and your riders might have to grab their horses mane to keep them self steady, and will definitely have a sore bum the next day! Cantering is faster, but smoother. Easier to sit, but could be scarier to a new rider. Galloping is very fast and the rider has to stand up out of the saddle and lean foreword in order to gallop a horse and maintain balance. Another point: I see a lot of books and movies were horses only speed seems to be a gallop. This is very unrealistic, and annoying to people who know about horses. So I would suggest making sure your horses have more than one speed. ; )
It sounds like the horses in your story are very well trained, so I don't think your characters will have much difficulty, as long as their are brave, kind, and strong. Here are some important thinks about riding horses that your characters should know before they try:
Reins are for steering, not for balance. The reins connect to a metal piece in the horses mouth, so pulling on the reins hard is uncomfortable to the horse and unnecessary.
Kicking the horse is also unnecessary. It is okay to grab the horses mane if you lose your balence, horses don't have nerve endings in their mane hair.
On a well trained horse, your characters probably won't have to much trouble. Getting on might be hard, they will probably need to find something to stand on. Another pitfall they could encounter is a horse spooking. Even a week trained horse spooks fro time to time, jumping to the side, spinning, or bolting. A new riding could defininlty fall off from a spook. Horses can spook at all kinds of things: loud noises, sudden movement, small animals, or anything else that could startle or frighten them.
I would suggest reading some books and watching some videos or movies about horses too, so you can see what things look like, learn the words for horse things, and see how other authors write about horses without having to explain all the equestrian terms there are. I hope something in this post was helpful, thank you for visiting our forum, (Anyones welcome!) And Good Luck with your book!!!