Do you know what state your horse is from? I would contact the BLM in that state.
I did that years ago when I first bought my Mustang. I knew he was from Wyoming, and I wrote the BLM (found contact info on the internet somewhere) and gave the lady his brand number and she looked him up and told me he was from the Salt Wells Creek HMA (horse management area) and told me the date he was captured and everything. It was kind of cool!
So I know it can be done, but it's been about 5 years since I did it so I don't remember exactly how I did it. But the one gal who wrote me back was very nice.
Oh, and the certificate from the BLM that came with my mustang was marked "duplicate" so apparently they can issue duplicate copies of their certificate of title.
You know, you probably don't even have to know the state, because the numbers are probably for the whole nation, not just one state. So I would try to find some BLM contact info. On the internet and see if they can look the number up for you.