I heard that hot weather in the summer makes the pastel colors of the sunset sky more vivid and more red? Is this true? But I also heard that in the winter, the colors of the sunset sky are brighter and more pronounced. How could both of these be true?
A complex interplay of scattering (Rayleigh-scattering for particles smaller than the wavelength, and Mye-scattering for larger particles), sun angle and attenuation of light on it's path thorugh the atmopshere determine the sky colour.
(Linked in a similar question here) http://www.severewx.com/Radiation/scattering.html
So, bringing it all together, it is not the absolute temperature that determines the colour of the sky, but generally the state of the atmopshere at your place with its aerosols and moisture, be it winter or summer.
In addition to the atmospheric color effects described by a_donda, there can also be color variations in the sun itself during a single sunrise or sunset, which are again caused by atmospheric effects. Here too, gradients on temperature and density are more important than an overall hot or cold temperature. These gradients cause refraction effects that may magnify the ordinarily tiny separation of sunlight into its different colors, causing green or even blue colors to briefly appear in the rising or setting sun. Sunsets over water are a common setting for viewing such green flashes, but I have seen them at sunrise over Lake Michigan from Chicago.
The most common form of such a green flash involves a setting where cooler air is atop a warmer surface, which produces an inferior mirage like we commonly see in a desert or on a roadway. In this case, however, we are basically looking along the reflection plane where the mirage produces magnification and therefore makes the green flash visible.
The reader can learn more about green flashes here.