Color temperature plays a role to determine the look of a photograph. Not only does it dictate its feel, it has a psychological factor in how the viewer internalizes it. While most subjects tend to look better in warm light, there are situations in which warm light isn't right. Think about a foggy day or one filled with rain or snow. These three circumstances naturally provide cool toned light and would look awkward if one were to fool around in Photoshop to make them look gold, red, yellow or orange.
With regards to the psychological factor, warm tones connote comfort, heat, relaxation and peacefulness, among other feelings. For instance, even pictures of ice and snow that are created at sunrise and sunset suggest warmth regardless of the outside temperature. The photographer may have endured minus 30-degree temperatures with much lower wind chills, but the viewer of the image won't feel that due to the color of the light. Conversely, the viewer of the same scene shot on a cloudy or dreary day with a bluer cool tone will perceive the frigidness.
As evidenced by the accompanying images, color temperature, governed by the time of day, has a great impact on the "feel" of the photo. In the two photos made in Grand Teton National Park, the time difference was only 33 minutes, yet the warmth, feel, look, and mood of the photos are completely different. The dawn version has a much cooler feel than the one taken only a short while after sunrise. The dawn color is predominately blue except for the band of pink in the sky. Not long after the sun broke over the horizon, the scene took on a much warmer tone. In the seascape photo, the impending storm and ominous sky communicate a cool and unwelcoming feel. On the other hand, the photo of the bristlecone stump taken at sunrise exudes warmth and open arms.
To a certain extent, warm natural colors can be enhanced using filters or in post production. The same holds true for cool tone natural colors. I discourage you from trying to aggressively warm up naturally cool-toned scenes as it produces an awkward and less-than-natural result. If you're going for a special effect, then give it a whirl.
To get more of a feel for how the color of light impacts a photo, experiment with white balance presets in Photoshop to change the color temperature. Use the RAW converter to see what kind of looks the pull-down options in the white balance box provide. The shade and cloudy settings add warmth to an outdoor capture while tungsten cools it down. Fluorescent cools down the blues but punches up the magentas. Daylight and flash provide very similar results.
So what is one to glean from the above? Learn how to match the light to your subject or to a particular look you want to impart. The first step is to learn how to read the light and to become comfortable knowing what effect cool and warm toned light have. This comes from experience and studying images that are predominately one tone or the other. Shoot in conditions that provide both "feels," and study the effect. If the desire is to emphasize cool hues, cloudy and blustery days are a good bet. To get the best warm light, concentrate on sunrise and sunset. The bottom line is to get out and photograph in all kinds of conditions and apply what you learn to all future shoots.