Don't paint the cedar,it's beautiful. Change the fixtures, bring in more light. I don't know what the floor looks like but you might consider changing flooring. If you feel the room is too small, think about removing some of cedar from one wall or the ceiling.

Washing the cedar with a creamy pale tan paint will lighten the room, the grain will read through so you maintain the character. Paint the other pieces a charcoal tone - a paint like sw canvas tan for the walls / 2/3 paint, 1/3 water - storage / vanity and frame - sw grizzle gray http://www.sherwin-williams.com/homeowners/color/find-and-explore-colors/paint-colors-by-family/SW7068-grizzle-gray/

I painted cedar in one of my bedrooms and it was awful ... Had to rip it out and hang Sheetrock ... Big big mistake ...

This is a tough decision if you are not a cedar fan. Although a very beautiful wood, in its natural form/colour it will always close in a room making it feel smaller ( and a bit like a sauna). You have 3 choices really:
1. Leave it natural but change all accessories to something modern and light e.g. Stainless steel or white to match the fittings. With lovely white fluffy towels this could work and is your cheapest option.
2. Whitewash all the cedar but get professional advice and products so that the finish is good. You will still want to do something about the cabinet and mirror which n the photo appears to be oak/ oak effect - and won't match
3. Rip it all out, fix the ceiling and backing walls ( you really will not know their state of repair till you are finished stripping). This sounds like it will be your most satisfying option but will take the longest and cost the most.

This is a great project. Good luck

Thanks for all the great ideas!

That cedar wood is gorgeous! I hope you find a way to live with it.

The main things that need "work" are the vanity including sink and fixtures and the lighting over the sink. Think about at least replacing the top of the vanity with granite or slate with a vessel sink in hammered copper and a single faucet

Forgot to vote for not painting the cedar. Also, vanity lighting option. Most above mirror vanity lights are not very attractive but this might be the least offensive alternative.

Remove some but not all of the paneling?
http://houzz.com/photos/501649

http://houzz.com/photos/2716352

Or keep it and remove all other wood (like the mirror and cabinet) replace with lots of white.
http://houzz.com/photos/278595