It depends on what kind of "horse bow" you're going to make. There are dozens of versions and varieties. For everything you ever wanted to know about Asiatic bows and archery equipment I would suggest going to:
atarn.net/phpBB2/index.php
and spend some time reading, especially in the "Making Equipment" section.
For a simple "horse bow", you can make a board bow with glued on rigid "siyah" tips that will look Asiatic, like this one:
atarn.net/phpBB2/viewtopic.php?t=1018
Bows made exactly like this were used by the ancient South Chinese.
This guy basically used a $5 bamboo plank, simply glued on the siyahs with TBII and tapered the limbs equally from the handle to the siyah joint. Then he spiral wrapped the joints with real or artificial sinew. Your cherry would make good looking siyahs on a bamboo plank if each siyah was made from two thinner pieces of wood glued together with the grain at different angles, for strength.
You can get bamboo planks for $5 plus shipping, here:
mastergardenproducts.com/bamboo.planks.htm
I made a bow like the one pictured above, using weak bamboo from a culm I was given by a local furniture store (hey! it was free!). Turned out nice, but because the bamboo wasn't thick like the planks above, mine came out only about 25# draw at 28". You don't sand the rounded outer skin that is the back of the bow, except for two flat spots that you sand at the tips to make a good flat glue joint for the siyahs. You can thin the flat belly side to adjust tiller (draw weight) as necessary.
A bamboo bow like this is very forgiving for beginning bowyers - being one, I know!
NB. It's not "primitive" per se, but you can also make this kind of bow using a slat cut from "real" bamboo flooring made from edge glued strips of bamboo (not the veneer over artificial stuff).
