How to create a hotkey for opening a new iTerm2 window?

This is already built into iTerm2. See the Hotkeys section in their documentation.

  • Show/hide all windows with a dedicated, system-wide hotkey
  • Create a dedicated hotkey window.

    In its simplest form, it's a system-wide terminal window that you can open with a hotkey.

You can find these options in Preferences -> Keys

OSXDaily has an excellent write up on this (with pictures)