What would happen if the sun froze?
By freezing of Sun, I assume you meant that Sun will no longer supply us the solar energy or heat. If we lost the solar energy, Earth and all other planets will still be in solar orbits, but will not receive any heat energy from Sun. In such an eventuality, everything will become dark, plants will not be able to carry out photosynthesis and we will be in an indefinite ice age. So, on one hand, we will not have any light and, on the other, no food. This will result in drastic loss of life on our planet. Unless we can figure out another source of food, all the life forms on Earth will die out. Lack of light and heat will not be the biggest detriment to our survival, as we can use nuclear energy for heat and lighting (at least for small fraction of our current population). It is the lack of food that will cause our extinction, along with other life forms.
Hope this helps.