You cannot take the saddle off the donkey as there is no great need for this to be done on Shabbos. You can untie it and let it fall off by itself.

Chapter 305 Section 10

Animals cannot go out wearing a feeding bag. On large animals you cannot put on a feeding bag on Shabbos as you would be doing work for nothing since the animal can eat from the floor by itself. On small animals that find it hard to eat from the floor you can put a feeding bag on Shabbos.

Chapter 305 Section 11

An animal cannot go out with an ornament. Devices that are necessary but are not put on tightly and might therefore fall and be carried, such as goats that wear a sack on their breasts so they won’t get scratched, are not permitted.

All the carrying we mentioned relating to animals does not mean in a private place with no eiruv. Some say that even in a karmelis, such as today’s public areas, an animal can carry.