Jay Massey hunted in Alaska with sinew backed bows. He would cover the sinew(in most cases) with fish or snake skin then seal it with French Polish(linseed oil and shellac). Later he started using a special epoxy thinned with a solvent(hense Massey finish).
On the few sinew backed bows I have made I sealed the sinew backing(sinew and hide glue) with TBIII first, let it cure then add snake skins(with TBIII) and used Tru-Oil over that. If you know the weather is going to be nasty a good coat of car wax will help to repell the water.
It is the humidity that effects wood and not necessarily rain or even dunking in a lake. The moisture moves by osmosis and that is slow...going in and out.