First off, I'd Sheetrock over the beams. It would allow for some awesome lighting up there, and give a warmer feel. Even with that height, you will close the room up if you stain the wood ceilings to match the beams and floor. There are great colors that will enhance the style of the room, with out making it feel like a cave. If the overall design go the home is Spanish style, it will enhance it with light and color.

Is this what you have in mind

You may just end up with too much going on if you don't keep the overall theme in mind. I have really high ceiling too but no beams so I just painted the walls and the ceiling the same color. No easy feat I might add for a run of the mill DIYer. I wouldn't go so far as matching the floor though. Start with the wall color and if it is not going to change then leave the ceiling color the same as well and work on the scale of the furniture and the wall shelves/pictures. The wall size is screaming out for larger picture frame and larger accessories. Bring in pops of color with the accessories and make everything larger than life. Just from the picture the walls look visually overbearing compared to the shelves.

In your decision keep in mind that if the walls are one color the ceiling another the beams and the floor another then they have to definitely compliment and not contrast. Just curious is that a window at the top of the wall?

Thanks for all the feedback and rendering. That is a window up top which I also need to address.

I would definitely keep the beams. If you cover them you may regret that decision later on. Accentuate them! Show them off!

Here's a look at my living room for reference.

Window would have to be dropped to the proper height so the beam will not cut the view plane.

Two story windows do make a nice visual effect and it makes the whole room.
When I designed my house, I have a two story dining room and I also did all glass with a huge circle window in the middle.
Here is another idea

If anything, I would keep the ceiling in lighter wood color... I think that would make a big difference and it will make everything stand out.

But you are adding beams? I think a cleaner look will update and add value when you are looking at so much wood. That room needs a good electrician to show you how beautiful it is.