I can't see the link but the only thing I would use from solocomb on a horse with a thick mane it the solo rake it seems pretty good but for a fraction of the price you can get similar things from pet shops made for dogs that work equally well :) x
I have no experience with that, but I can suggest a dematting comb. It works well for getting out burrs and matts and both dogs and horses. I have one for dog grooming and use it on my horses' tails and manes. It has small razors on it so with each brush some of the hair comes out. I'm sure if you brushed with it it would thin the mane fairly well. You can get them at most stores like Petco or Petsmart in the grooming section. The one I have looks something like this;
I believe it would probably serve the same function as the one you posted, but I wouldn't go crazy with it. I've only used it to untangle hair, and it basically thins the hair and the shorter hair sort of blends with the rest. If you start with a bit at the top and then take more off at the bottom it might look better. (I am only a dog groomer, I've never really groomed horses too much aside from my own, so I wouldn't entirely take my word for it unless you use the comb for dematting/"deburring" purposes. ;])
KV, when my Dad was showing, he refused to pull the mane on any of his horses. He would use a thinning comb very similar to that to shorten and thin it out in lieu of pulling. He said that way, he didn't have to deal with the constant re-growth that you have to contain because it wants to stand up straight. Not to mention the fact that it's faster and easier than pulling.