I have no clue where this ridiculous tradition came from to thin a mane or tail by pulling out hairs. From the time before scissors were invented? It makes no sense and is unkind to horses.
Of course it hurts! At the time it is pulled, and it’s sore later. What if someone styled human hair by pulling out the strands that were too long? Ouch !!!
Beauty supply stores are everywhere and they sell to anyone (such as national chains Ulta and Sally, and many local stores as well). Buy ‘thinning shears’ (they have other names as well), with ratcheted teeth. They cut part of the hair in hand, but not all of it. You can find them from $25 to $300, and the cheap ones work fine for horses.
Like this
https://www.sallybeauty.com/hair/she…hapers#start=1
Shears can also be ordered online in many places, but then you’ll miss out on fingering the wonderland of stuff in the physical beauty supply store. Although you’ll save maybe $100 extra-spend bucks if you don’t go in the store and browse all the amazing things they have. 
Then back at the barn, comb out the horse’s (clean) mane and divide it down the middle, pushing the sides down on either side as best possible. Use the thinning shears as close to the horse’s neck as possible to thin the mane. Same effect as pulling, without pulling. You’ll need to thin more in the thicker part of the mane to make for neat braiding.
Cut from the middle of the mane, right next to the neck itself. Same as pulling, don’t take off the hair at the top of the mane as it won’t braid properly. This takes out the hair from the base root just the same as pulling, without hurting the root inside the skin (that’s what is painful about pulling).
Then comb it all over to one side (lots of combing to remove the loose hairs). Use regular scissors to nip off the too-long ends, with little cuts that thin the end of the mane, and avoid a banged look. If you cut straight along the edge (if it’s long enough to justify that), don’t take off too much. You’ll want to go go back and make little cuts back and forth to thin the ends of the mane and remove the ‘bang’ edge. Don’t go crazy with this as it can become very short.
I’ve been doing this since I got back into riding many years ago, having vowed never to pull another mane. I’ve been complimented on the horse’s neat appearance, and on neat braids. Not once has anyone ever said “it looks like it was cut with scissors”. And I know horse people who would say so immediately if they thought so.
