I don’t think using a display to white balance your camera would be a good idea.
You are on the right track though. Although the white balance setting you would need to achieve the effect you are looking for would not be the same every time (even if you could get a screen to display an accurate white).
I would recommend thinking about what the dominant light type is. In your tree grove example the dominant light was most likely shade with streams of warmer light. If you want to capture the feel of the warm light set the camera on shade (in this example). If it where a sunset you could try daylight. better yet try setting the camera to a specific kelvin setting (if you have that option) that way you could make small changes to achieve the effect you are looking for.
This is an example of one of the major differences between a camera and the human eye. Even with a good white balance setting the difference between the two types of light will be more pronounced than what you will see because of the way our brains compensate for these differences.
Saving a RAW file and making these corrections on a calibrated display would be the best option because even if you were able to get the effect you were looking for on the cameras display you would still need to correct the file some later to achieve the same look in print or on your computer screen (the cameras display is not calibrated).
Hope this helps,