Cygwin does provide its own minitty terminal but the Cygwin environment can be made to load in the windows command prompt cmd.exe by executing the Cygwin batch script Cygwin.bat.
The following registry edit will make it so cmd.exe executes C:\cygwin64\Cygwin.bat on startup thereby transparently loading the Cygwin environment every time a command prompt is started.
Windows Registry Editor Version 5.00 [HKEY_CURRENT_USER\Software\Microsoft\Command Processor] "AutoRun"=hex(2):43,00,3a,00,5c,00,63,00,79,00,67,00,77,00,69,00,6e,00,36,00,\ 34,00,5c,00,43,00,79,00,67,00,77,00,69,00,6e,00,2e,00,62,00,61,00,74,00,00,\ 00