Interestingly, it can seem that way.
We say True Summer colors are purely cool. But next to True Winter colors, True Summer colors actually appear a tad bit warmer.
This has to do with the fact that True Summer colors are less saturated --i.e., more greyed.
To desaturate or "grey" a color, we add its opposite color. For example, to mute a purple, we add yellow.
By doing so, we draw the color a tiny bit across the color wheel, bringing it closer to the warmest color on the wheel. So, since it's closer to the warmest color, it appears to be a bit warmer.
Here are some True Summer pinks:
And here are some True Winter pinks:
Those True Summer pinks look a little warmer, don't they? The warmth is a result of the tiny bit of yellowish-greenish color that is added to the True Winter pinks to desaturate them.
Here's the practical application of this for you: if you think you're a True Summer, but those "purely cool" colors still feel too warm for you, you might want to try True Winter.
Still unsure of your season? Try affordable at-home draping.