No, :w is a /usr/bin/vi command. Use the combination control+x to exit. You will be prompted to save the file if you have made unsaved changes.
Nano is intended to be a bit friendlier / simpler to new users than vi/vim or emacs which both cater to more power users that have spent time learning how to use them effectively.
To get started in nano - look for commands along the bottom of the window when nano is open. (^ stands for the control key)
^X (F2) Close the current file buffer / Exit from nano
^O (F3) Write the current file to disk