When I ran a crew turning cow wrappers into snowshoes, we preferred to use leather from the back for the center portion of the snowshoe, and the thinner side and belly hide for the toe and tail.
Our treatment: The entire cowhide was soaked in a barrel of lime water until the hair loosened. We then would pull it out, and drape it over a smooth horizonal beam, and scrape the hair off. This was a balancing act: Soak too long and the hide was weak. Too short, and the hair wouldn't come out.
Hide was then cut into pieces about 18" across, immersed in water and frozen to store it.
The fastest way to cut it was to freeze it flat, then use a bandsaw. (DO remember to clean the bandsaw.) You can also cut it with a very sharp boning knife. Use a fusee to touch up the edge every few feet.
Snowshoes are laced with the hide sloppy wet. As it dries it shrinks hard.
If used in cold weather, you don't need to waterproof it. Accounts I've read of the native culture indicate that snowshoes were regarded as disposable items. They would make a pair for the conditions then present, use them for a week or a season, and discard, or recycle. My bet is that they used some form of waterproofing on them. On canoes they used a mix of wood ash, spruce pitch and fat. I bet that they used some form of fat and pitch on snowshoes too in warm weather.
At one point in my past I was snowshoeing 5 to 30 miles a day. I had 2 pairs of snowshoes so that one pair could sit an extra day beside the stove drying out. Wet babiche has little strength and wears away very quickly. In addition a soggy snowshoe is like having 3 inches of porridge on top of the trail sucking energy out of you.
You can use nylon parachute cord for lacing snowshoes, or if you can find it 1/16 x 3/8 nylon webbing. Nylon will get a bit stretchy when soaked in warm water, but in general you have to pull a lot harder to get enough tension on the snowshoe.
Cord is a good learning medium. Your first center takes about 3 hours to lace, and you will be undoing nearly as much as doing. (Follow an existing snowshoe) Don't lace for real until you can get it below an hour. My crew could do whole pair in about 2 hours. The pros can do a pair in 45 minutes.
Use a bench. Sit on one end of the snowshoe, with the part you are working on in suspended space.
the lacing is slippery. We kept 8 inch chunks o broken snowshoe frame. Take two turns around that, and use as a togggle to put tension on the lacing.