Only in rifles that were not properly free floated, and we'll bedded.
Maybe if they were completely water soaked and then frozen, but otherwise good hardwood stocks work fine.
In my reading in the past, I believe either OL or F&S, they did these type of torture tests and found that synthetic had no appreciable affect and the woodstocks were off as much as 3" at 100yds. They soaked, froze, etc. the stocks and then did tests. Google would help you find them. I hunt all synthetics now and can't offer a recent personal anecdote.
I think it's mostly an issue for older rifles that were made before free floating or proper bedding became common. I have an older (1950's) custom made Mauser .270 that was my grandfathers. It has a beautiful birch stock on it and it still shoots close to an inch at 100 yds with the same original Lyman 4x scope. But every once in a while it just does "weird" things when it gets cold and/ or damp out for an extended period of time. The barrel is not free floated, but it is bedded directly into the wood stock (no fiberglass, just straight wood).
Good bedding, free floating, and sealing the wood anywhere that it isn’t sealed will certainly help. My dad had a gun that was bedded and free floated and part way through a hunt he looks down and the stock had warped to the point that it was touching the barrel, and took considerable pressure to bend off of the barrel. The more grain the wood has, the more stable it will be because it has to fight itself to warp. If the grain is fairly straight and boring then it doesn’t take much to warp. These days most guns come with synthetic sealers that keep moisture out to a pretty high degree. Pull the gun out of the stock and check the barrel channel. Sometimes that is completely bare wool.
Wood warps - warped wood can touch the barrel - wood touching a barrel=inaccuracy. With some guns, and in some conditions, a simple barrel floating and good action bedding is the trick. Good sealing is obviously important as well. Some guys will even epoxy-bed a steel rod in a channel they chisel out the length of the stock forearm. Wood is pretty, but I hunt more synthetic than wood these days. (but I do have a few I can't give up - a 30-30 lever action, a 1885 highwall, a beretta 12 ga)
All I've ever hunted with is wood stock's. Never one time in my life has one moved on me that I could tell. All my rifles have been free floated except a Sako L69 that was bedded tight all the way, it never moved! All my rifles also get the action area finished and under the butt plate and pistol grip if it has a plate. Sealed wood does not move normally. Of course if your one that treat's his rifle's like garbage, could be they will move. In order for moisture to effect wood, it first has to get into the wood. Well sealed moisture doesn't get in there. As a kid, had an uncle that seasoned oak and walnut. He painted only the ends of the wood and the stuff never twisted on him. That was in Oregon's Willamette Valley, about the wettest place on earth. Even so I seal every bit of bear wood in my stocks. Bedding with that Sako tend's to make me believe even bedded tight, if well sealed the wood won't move. As for free floating, is it moisture or hgh spots that throw the shot off? Same with bedding the action. If it's not well bedded, does the action alien the same way every time? Of course my though's may be tainted as I can't stand the sight of plastic stock's!