I realize that this thread is pretty old but the challenge (wooden window in shower) will keep coming up for new owners. Most of the 'solutions' presented so far are not solutions - in fact they will cause far more damage than just letting the window get wet from the shower.
At we work in a lot of homes in the SF Bay Area that are older Victorian (read this as 'all wood'), also we are based in Mill Valley (North of the Golden Gate) which is known for it's constant dampness and high incident of mildew and dry rot. We do a lot of dry rot repairs and what they all have in common is a lack of proper ventilation. So - that being said here's a list of the three best ways we've come up with to handle this problem:
1. Bathroom exhaust or ventilation fan! Install or upgrade the bathroom fan. All those baffles and shields and shutters will only make mold and dry rot more of a problem as they block air movement in the area needing it most. You need MOVING AIR to dry out the water and remove the thing that mildew and dry rot need most (water).
2. Automatic fan switch! Along with #1 you need to install an automatic timer on the fan so that it runs for at least 20 minutes (you may need more) after you leave the bathroom. It's better to install an automatic sensor that turns the fan on whenever anyone is in the bathroom than rely on yourself or others to set a manual timer. The 'occupancy presence sensor' type switch will never forget to turn the fan or or off. They have some adjustability as far as how long they will run but 20 minutes is the very least amount of time needed to properly vent a bathroom after a shower or bath.
3. Seal all wood! It's a common mistake to think that simply tiling a surface will 'waterproof' it. Lots of boats are wood. So far as I know no boats are made of tile. Seriously though... Remove all caulk and then sand all paint from the wood. After you are sure all the wood is exposed apply a marine grade two part epoxy (West System is a good brand -but there are others..) to all of the wood surfaces including the muntins, grid or windowpane dividers, and all sill and frame parts. Make sure the epoxy soaks into all the surfaces and once it's dry, wash it with a little soap and water before priming and painting with a marine grade oil paint. Don't cheat on the epoxy or the paint. Be sure to wash the epoxy before painting it and wait at least 24 hours between coats of paint.
Once you have all the wood sealed and painted then apply any needed caulk to the joints. Be careful about using siliconized caulk as it actually seems to encourage mildew from what we've seen. Latex or polyurethane seems to be better in wet environments that are exposed to air. (silicone does better than the others when it's under water as opposed to exposed in an wet air environment.
*** if your house is older than from 1980 you need to take care when sanding as the paint may contain LEAD which is very bad for people and other living things and need to be handled carefully.
Q