I would worry more about protecting the metal than the protecting the wood. You hear more people complaining about rust than people complaining about a bit of rain destroying their stock. This is something that I would only worry about if I lived in a swamp or a state where it rains almost every day. The metal is going to rust from moisture quicker than your stock will mold/mildew/rot.
There are a number of things you could seal it with, some more permanent than others. Like Barry said, a wax coating would repel water. An oil finished stock will resist water damage because its oil finished. Your stock may already be oil finished. Some type of varnish would be a more permanent option.
I don't know about its use on gun stocks but there are some super hydrophobic coatings that water practically jumps off of. Coat something, submerge in water, and it comes out dry.