This looks more complicated than it actually is. However, like most braids, it will never look right when you actually do it... this can be solved with practice.
As for the braid I will do my best to explain.
1-you decide how many knobs you want. Lets say we want 8 knobs. So we will section off the mane into 8 equal sections. I will demonstrate on my own hair, mimicing 1 section
2-you you divide each section into 2 LAYERS that's one on top of the other
3-you braid the top layer in a plain-simple braid
4-reapeat 3 with the bottom
5- wind the top into a tight ball and rubber band the ends so the knob remains small and tight (my hair is to slick to knob, so you will have to pretend-sorry-)
6-repeat step 1-5 with each section
7- take end of braid and wrap it around the knob next down the horse's neck
These braids are good for slightly longer manes. However, Lacey's mane grows like a weed, so it was a bit too long but they still look fairly good
These braids require thread or yarn, no way around it! (Or those new braiding wires)
Start by braiding as if you were going to do hunter braids(youtube hunter braids on how to braid in the yarn):
Then, using a latch hook or whatever home-made tool you might have, pull the yarn from the first braid up under the third braid, make a few knots around the top to secure it in place:
(I didn't have anyone to take a photo of using the latch hook, but again youtube how to do hunter braids, they will show you)
A slight variation is to push a little bump up to make a combo of scallop and dressage button braids. This photo also shows looping the second braid under the fourth braid:
Finished product (without the buttons):
I had also done exactly the way in your OP photo but simply pulling the first braid under the second braid instead of skipping to the third braid.
Hope it's easy to understand!