You want to varnish the whole thing - wood and lacing, top side, underside, seat bar ends until they won't absorb any more and as much as you can get down into the bolt holes with multiple applications. The varnish is what keeps the hide from stretching in use due to moisture absorption. On a long trip in wet weather, you will probably still get some temporary stretching. It will usually go away after they have dried out again.
A couple other things to know about rawhide: It comes full grain (the full original thickness of the hide) and this type is the best quality - strongest and resists stretch the best. Most high quality rawhide products are full grain. Leather and rawhide are also available as split grain. This stuff has been split into layers. "Top grain" means that you are getting the natural top surface (the best and toughest part of the hide) as well as some of the stuff underneath the top. Then there is "split grain" which generally is all made from just the under layers (a better translation for split grain would be "somebody else got the best part of this piece - so don't expect too much from it". A lot of rawhide vendors these days sell both full grain, and also a top grain split version at a lower price. It is worth the difference to buy the full grain version for products like canoe seats and snowshoes if you ever need to replace your lacing.
There is also a top side and a bottom side to the lacing strips. Usually, the top surface is smoother, but not always. As they dry, it is not unusual for them to curl a bit, and they will usually curl away from the top side. By making sure the top side is positioned upward (where you will be sitting) the stuff tends to be somewhat less abrasive to sit on, as dried rawhide strips have pretty sharp edges.
For a short time in their very early days, Mad River Canoe was hooked up with Tubbs of Vermont (the snowshoe company) and the boats had snowshoe rawhide seats made at the Tubbs factory. I owned one of the very early "Malecite" canoes from this period (a dynamite little boat that I wouldn't mind still having). We took it on a ten day long trip into Canada and during that time, both of us wore holes through the seats of relatively new Levis due to abrasion on the rawhide seats. Ever since I've started going over the rawhide top side pretty carefully with my hand on seats before varnishing, looking for sharp edges and dulling them down a little bit with a scrap of sandpaper. It's not a huge deal, but it helps and if you're getting ready to revarnish your seats it may be worth doing before getting out the brush.
