Magento 2.2 is not working in PHP 7.2.0

Unfortunately no, PHP 7.2 is not officially supported yet. You can see below list and information from Magento dev docs about the system requirements.

1. Magento 2.2.x supports PHP Versions below:

• 7.0.0, 7.0.1 - Not supported
• 7.0.2 - Supported
• 7.0.3 - Not supported
• 7.0.4 - Supported
• 7.0.5 - Not Supported
• 7.0.6–7.0.x - Supported
• 7.1.x - Supported

http://devdocs.magento.com/guides/v2.2/install-gde/system-requirements-tech.html

2. Possible Fix:

As stated in the warning the each() function has become depreciated as of PHP 7.2 you can see more information about this here:

http://php.net/manual/en/function.each.php

To fix the error however you can try swapping the each() function with foreach() as this is supported in PHP 7.2 but i cannot guarantee that more issues will begin to arise.