Making one of these should not be to hard. I have been making bows (hand bows) for about 20 years. In my early days I did some work with sinew and horn. I kind of gave that up due to the fact that at normal draw weights, wood is just a lot more efficient. Horn bows start to shine at higher weights due to all of the extra mass not being as important then, and I do not care much for shooting bows much heavier than about 85 punds in draw. Horn and sinew are a lot heavier than most wood. All of the problems with making a composite bow, like the turkish or korean ones, do not really exist with the crossbow. No stability issues or anyting (or at least not like with those highly stressed hand bows)...just need to make it thick and short, so it will be expensive in terms of horn and sinew. Tillering should be fairly easy if you make the core to very careful measurements, then add the sinew. once it is on if you sand it to make sure each side matches, it should be pretty close. It should be not so hard to find horns long enough to have without splicing in the middle. If you have only short horns, you can cut them apart spiraly and then flatten them, and if the horns are long enough, you can cut them up the middle and make one big sheet to cut the strips from. Either way you end up with the same product. having the grrove match on the sides is good, helps get a strong glue line to handle the shear force. In a sense, it is not such an issue here due to the extreme amount of sinew that is used all the way around the bow. that will hold almost anything together. As thick as the sinew on the backs are, the other parts should not be dealing with much tension, just with shear force and some compression. Horn is great with compression. In fact, these should be a lot safer to use than steel bows. with that much sinew, you should not have a tension failure unless you dont handle you glue properly. The sinew will be streatchy enough and the whole bow really will not be bending very far. I plan to start one as soon as my wife lets me spend the money on the horn. I just got a house, so now have a garage to work in at nights.... all those years in apartments made life hard on a bowyer (wood chips are hard to get out of carpet). As soon as I get the horn (probably in a month or two when we have some moeny saved up after spending all of it moving in here) I will make an order for some horn and put photos up as I go. I have always wanted to do one of these. I have also been thinking to do one with steel, but seems like to much effort and expense (and I have almost no metal working experience). I think two extra large bull horns will make enough material for a bow.
Seems like the thing to do is to cut the hollow section out and boil it for a couple of hours, then flatten the whole thing into one sheet. If you can get your hand on an extra long bull horn (like the ones out in texas) you should have more than enough length. Then you can cut the strips out to any size you like. the grain orientation of the horn (they have it jist like wood) will not matter if you are laminating many thin strips together, they will hold each other straight. Some composite hand bows were made this way to keep them from twisting as the horn tried to get back to the original shape. I suspect that type of horn is not all that big a deal. It seems that way now, since everyone loves the water buffalo or gemsbok horns. I think they are the thing now because peple do not like working with twisted horn, or splicing in short sections. the photo above sure looks like cow horn. If they were make in large numbers in the middle ages, then I would be that cow horn was the one used. Others may have been used as well, but having as strong supply of material for these things would have been a matter of national scurity.
If you make them to the original size, I would expect it to be very strong in draw weight. they look massive.
I notice that both of the diagrams above have the wood on the belly. That is interesting, if you do it that way, the horn does not serve a function. It jsut sits in the middle of the bow and deals with shear forces. since it is on the neutral plane of the bow, it would do very little in terms of compression or tension. I have seen some horn bows that show a more normal cross section of either horn directly backed with sinew or with the wood as the middle of the sandwich, so that it is only making a spine to glue the other parts to. this would make the whole things a lot easier to handle as you work. the other ways (as shown above) will work fine, otherwise they would not have done it. I suspect that in those cases, the real work is being done by the sinew on the back. As long as that is properly applied, it can make up for a lot.
The thing to keep in mind when doing a project like this is that all the people who say it is too hard to do have mostly never tried. People did this hundreds of years ago. People now are just as capable and smart as they were (and we have power tools).
On another note, mentioned in posts above. I have heard that whale baleen does make good bows. Naturally I have never used it, but I think it can be obtained from some sources (like natives who are allowed to still hunt whales). Might not be worth the troble of explaining your bow, made of whale parts, to the police though.