Running braids and double braids are great for long manes, and look so classy
You could do a tight running braid or maybe you could make tiny braids instead of thick ones
Careful if you shave a part of the mane, it can be a disaster!
A long time ago, I had a mare with a very thick and long mane. I have tried some different things. First, I did fat button braids. They looked good, but they were both huge and very close together. I had to put a lot of hair spray to be sure they will hold during the show.
I also tried parting it in the middle and putting a row of braids down either side. It was very beautiful and creative but honestly, it took me a lot of time.
You can do a French braid, I saw Amy gave you the link of a video, it could look nice on your horse. Running braid should also be right/
Good luck and...be patient!!
It is not he case of the horse I ride but a friend of mine has a mare with extremely thick and double mane (like ponies). It is a nightmare for her! So she tried to shave half of the mane and then braid the "last" part of the mane, it was so much easier. As her unshaved mane covers the shaved portion you cannot tell she had half of her mane shaved off even when you braid it!
So my advice would be to shave a little at a time. Take your time.
If you are too insecure to try it, you can do nice big button braids. It looks better on long mane. The secret is to really tight the hairs, you won't hurt your horse, do not worry. If you do not tight enough the buttons, they will untie as soon as your horse starts walking!
Maybe you can take a look at this video, the result is really pretty. https://www.youtube.com/watch?v=H-qaLoDEb4E
The horse has a quite long mane and this type of hairdo hold better on thick mane :) The key is to really tight the braid since the beginning!