No need to go the crappy plastic route. The key to preventing problems with a wood stock, in cold and wet weather, is ensuring that the wood is properly and completely SEALED. If sealed, there will be no moisture change possible in the wood....and no problems related to that.
Most wood stocks sold with off-the- shelf rifles these days are finished with polyurethane. That is as good as it gets for a moisture resistant finish. However, very few such stocks are properly finished INSIDE the inletting. That is where most of the problems begin. Moisture gets in, soaks into the wood, etc. etc.
The solution is very simple. Ensure that the stock is sealed, inside and out. So, I would highly recommend adding several coats of poly to the INSIDE surfaces of the wood stock (ALL of the inside surfaces)....as well as touching up any imperfect areas on the outside surfaces. You can also wax the outside, for additional protection.
Be sure that ALL areas are sealed. This includes small areas often overlooked, such as around sling swivels, etc.
If you have a wood stock with an oil finish, then it will be somewhat more delicate and maintenance-intensive, but still doable. I would still use poly to seal the inside surfaces (no one will see them). Then, add several coats of wax to the outer surfaces.
More maintenance will be required with a wood stock - that is a fact of life. Be prepared for it. If you can't handle that aspect, then better to go the plastic crap route.
The point is, people have been taking wood stocked guns into the field forever, with no problems. You simply have to look after the details and do the maintenance. For myself, I can say that I have never had any problems with wood stocks in the field and I have had them out in rain, snow, you name it.