Just to clarify, water requires a nucleus to start the freezing process. If water is impure because of particulate matter, it will still freeze at 32 F, and the particles will provide the nuclei so freezing will start quickly. Once begun, the ice itself continues the process.
If water is impure because of dissolved material such as salt, that will lower the freezing temperature. Adding salt to ice lowers the freezing temperature as far as zero F, which was used to make ice cream before mechanical freezers were invented.
If water is totally pure, the freezing temperature is still 32 F, but if there are no nuclei to initiate freezing, it will stay liquid below the freezing temperature. In such “supercold” water, any small disturbance is sufficient to act as a nucleus, and freezing will commence. I have seen a test tube of supercold water freeze solid in the blink of an eye simply by speaking to it. The tiny vibrations of the voice were sufficient to start the process.