If you take care of your firearm, that's the complete firearm including the stock, you won't have any of these bad effects from snow or rain. I hunt in the thick woods, in the cold, snow and rain and have never experienced any problems with my wood stocks. I am however one that spends some time on the care of my rifles. If it gets wet and you leave it wet after you get home it can cause damage. I also own only blued rifles. My 1895SS looks almost like it did when it came out of the box on day one.
I don't know about anyone else but I have found that applying some lubricating oil to the stock as well as the steel helps to preserve the like new look. It also seems to minimize the appearance of any dings or minor scratches that you might pick up over the years.
Besides, wood does look and feel better.