With horse hair this is difficult because you lose valuable hair length in the knot.
After making many, many bracelets now I have found that the best way to tie both ends it to do the following:
Once you have the hair where you need it to be on your kimihimo disc, gather it on the underside where the braid will be formed. At the point where you want the braid to start you can place some glue on the hair. I use E6000 or superglue.
Now get some thread tie a small knot then wrap it around the hair on top of the glue. You can knot it a couple more times then leave it to dry.
When dry, the end of the braid will be secure enough to start braiding and you can attach a weight with a paperclip or bulldog clip to help maintain tension in your project.
In this photo you can see a close up of an end, glued and tied. This will hold the bracelet together and at the finish you can trim the glued end to the length you need to fit your end cap or crimp finding,
Here is a video showing you how hair is sorted and fixed for a 12 strand rounded flat kumihimo braid