Thanks guys, this seems to be a little more clear now.
I get my horn from a scottish supplier (highland horn), but sadly he does not send to the US, as far as I have understood. That's for water buffalo, anyway.
I've been looking through my books, and found a very interesting appendix in the book "Native american bows" by T. M. Hamilton. There's a description of ten horn bows from the US national museum. They give dimentions for the middle, midlimb and tips for most of the bows, and also some thoughts about construction and sinew thickness. Some of them are considered to be made with cow horn, while others are made with more the more conventional sheep horn and antler. I wonder if they might have misinterpreted some of them as cow horn?
Anyway, I will go through the text once more, and decide upon which set of dimentions I will use. I'll post it in a while.
Bowman; I was not able to find any suitable long horn for the bow, but now it seems that it is authentic to join two of them in the middle. I'm sure I've got a pair for you, unless you want to make a one-piece bow (too).