The good news is the answer to this is the same as it is for Western clothing and make-up: it depends on your skin tone. The bad news is, a lot of people don't really know what skin tone refers to and needlessly restrict themselves to either "cool" or "warm" colors when the truth is they can wear a lot more than they think.
Skin tone refers to the overall tone of your skin, which is going to be either warm or cool or in a few cases neutral. This is not the color of your skin: ivory, fair, beige, ebony, etc. It's the underlying tone that looks either olive or yellow (warm) or blue or pink (cool). A good way to tell, if you're not sure, is to look at the color of your veins on your forearm. If they appear greenish, you're warm. If they appear blue, you're cool. If there seems to be a mix, you could be neutral (if any color of any kind looks good on you, you're this elusive third category).
Here is where confusion sets in (and you see it in a lot of places, including mass media). If someone has "warm" tones, the conventional wisdom says, they should wear warm colors (red, yellow, orange, brown). If they have "cool" tones, they should wear matching cool colors (blue, green, purple).
However, just like your skin, every color has a tone too. There are "warm" browns (with underlying red, orange or yellow tones) and "cool" browns (ones with underlying true blue, purple, or green tones). You can even have warm and cool greys. Colors that seem to shrink into themselves or move back away from the viewer are "cool", and those that seem to pop out at you or move forward are "warm".
To bring this back into clothing and kimono (and make-up), if a "warm" person wears a "cool" red, they're going to look off. The same goes for a "cool" person who chooses a "warm" green.
For the non-artists out there, I may sound like I'm nuts, so let's do some picture examples. Your monitor may vary a bit, but here are some kimono that are the same color, but different tones.
I chose iro-tomesode, a step down from kurotomesode in formality, and michiyuki, as examples, as they haven't gotten much love here on the blog. Iro-tomesode are just like kurotomesode, with patterning only along the hem, except they are colors (iro) instead of black (kuro). Michiyuki are just coats worn over kimono when going outdoors.
Before reading the caption, can you guess which is warm and which is cool?
Purple: "Cool" purple, with undertones of blue, is on the left. The "warm" purple on the right has undertones of red.
Red: While both are red, the one on top seems to recede back away from you a bit, marking it as "cool". The "warm" one on the bottom seems to move toward or pop out at the viewer.
If you're having trouble determining which ones are which, don't worry! It can make you go cross-eyed at times, even if you're used to dealing with colors in art or other areas.
The next time you're out shopping for clothes, take several pieces that are the same colors but different tones and try them on (maybe three or four red shirts and four more blue dresses). You'll notice which ones make you look washed out, sick or sallow, and which ones look nice against your skin, and with the items all next to each other it should be easier to see which feel "warm" and which feel "cool".
Once you figure out if you're warm or cool, look at something across the shop and decide if it's warm or cool. Then walk over and place your arm against it and see if you were right. For example, if you're a cool person and the item is cool, it should look fine. If it doesn't, then it was a warm-toned piece.
After some practice, you'll be faster at picking out not only kimono that will make you look great, but clothes and make-up in general. :) Happy shopping!