The combo of white trim and wood floor / ceiling /beams means you are somewhat limited in your choices. Green works with both but I don't think green will work well with the blue green gray stone at the hearth. Blue greens would be bad with the wood unless you want a real cottagey look. They have a kind of burlap that has warm enough undertones to harmonize with the wood but work with the white. . Creamier off white trim would give you more options. The new thing to do with wood (everything old is new again) is white walls - dark off-whites are really great for this . . . like bm maritime white .. if you have a lot of colorful art, that is a good place to go . . http://www.benjaminmoore.com/en-us/paint-color/oc-5
You can try some of the pine / spruce green undertones in the stone .. greens will work here
http://www.benjaminmoore.com/en-us/paint-color/antiquejade looks to be the perfect shade for the stone and is classic but very blue for green . .
or try aganthus green . .
woodlawn is starting to be too blue but you might try it if you love a cottagey look ..

This is not quite a burlap tone . . not quite that deep but a chocolate would look great here with blue-green / jade accent tones to pick up the stone and you could probably go not so warm . .like taos taupe . . http://www.benjaminmoore.com/en-us/paint-color/taostaupe#ce_s=taos taupe
this is cooler and should work better than what you have going but I suspect you are tired of all brown tones here . .you have a lot of natural light, so you can easily do darker tones . a dark stand in for navy / blue gray would be fresh . . like bm black pepper . . really allow the architecture to read out . . white and wood and navy / dark blue are always good . . a denim tone would similarly work if muted enough . . bm cloudy sky or steep cliff gray would be even better with the stone and wood . . straight blues are going to be more friendly here than blue greens ..

because the greens you have are green blues . . forest / spruce in that stone . .

hope this gives you a range of options you can find some direction in . . . add baskets and shades of blue and white and you have lots of places to go with accent colors . . some years / seasons red and white, forest and white, dijon and white to echo floor . . could use amber tones as accents with these building blocks. . with the current nautical craze and the architecture that feels a bit like a boat . . one of the darker blues would be my pick for the tall room and lighten it for the fireplace area cloudy sky and smoke . . http://www.benjaminmoore.com/en-us/for-your-home/rooms-by-color/beguiling-blue-entry

Try some of the paint sites where you can upload a photo and change the paint color to see what you like. Personally, I'd probably go with a neutral like ivory as previously suggested and go bold with color in art and decor.

What a beautiful room.

Great colour suggestions by libradesigneye. While someone is up on a ladder, I would paint the tongue and groove ceilings (a paler shade of what you put on the walls or white like the trim) to make the floors, beams, and stairs stand out and get rid of the slightly Swiss chalet look.

Wow! Thanks to everyone who commented. We will take all of them into consideration for sure.