I'm thinking a warm gray...it would accent the mirror and go beautifully with the color of the fire surround and the gray floor. You could do the chimney breast (the bumped out wall) in a slightly darker shade that the other walls. As noted above, look at the Affinity Colors from Ben Moore as your inspiration, then you can look at other manufacturers. Also, not that you asked, but replace the "feathers" on the mantel with something else...they're too close to the look of the mirror and almost look as though they have fallen off...use them elsewhere in the room, grouped together.

Can you attach a photo / link of the sample of the floor tile being used?

I have some suggestions, but none are cream tone. IMO, North facing rooms, because there is so little sunlight, need warmth which most light colors do not give for the chilly North room. BM Leapfrog accented with Asian blue and whites; BM Goldtone accented with cream and a painted blue ceiling; BM Slip accented with white and a really dark green velvet fabric.

Matt finish walnut will show pretty much everything...the yellow 'doodle hair will show everytime it lands. The good news is everything is so dark you will only see half of the dog hair. A ligher floor in a dark home will have the same effect as a dark floor in a well lit home. You might want to look at a floor that is stained (like white or European Oak) with a mid-tone brown (2 steps lighter than walnut) and you will have your crisp definition between wood and wall AND you will have a floor that is more forgiving with 'doodle curls. And be aware that many people find a matt finishe VERY hard to live with. It shows every hand print, paw print, nose print, "skin" print you can imagine. Skin oils are SHINIER than a matt finish = shows up every time a finger, toe, foot, dog pad hits the floor. Everytime. A satin is easier to live with.