Quick counter: lower kelvin lights are terrible for color reproduction. Pure sunlight is around 5000K, and has a CRI (color rendering index) of 100. Switching to warmer (lower kelvin) lights is going to also alter your CRI, and will change the way that you perceive colors. If you need high color discrimination, that's going to be bad.
For outdoor lights, in most cases that's not a problem.
Usually. In most cases, you aren't going to notice just how much the colors have shifted, because your brain automatically adjusts. Youre perception of color is usually how colors appear relative to other things; you will see a red as red because your brain is comparing it to other objects with a known color. OTOH, if you're taking photos under poor lighting conditions, you'll see a significant shift in color. If you've ever taken film photos under fluorescent lights, you'd see that everything looked sharply green, when you don't perceive them as being green at that moment. (Digital cameras often make color adjustments, and the sensors are often not as sensitive as film can be.)
Going to an extreme, if you use a red filter on a light source, all colors are going to end up looking brown and grey; switching to red lights does the best at minimizing light pollution and loss of night vision, but at the cost of most color information. That's not bad, just a thing to consider.