This is a partial answer at least. The background of the text area (not the header) can be set with
\setbeamercolor{note page}{bg=white}
changing white
to whatever color you like.
Another option is to change the template used for the note pages, plain
is text on a white background, no header:
\setbeamertemplate{note page}{plain}
I haven't figured out how to keep the header and change its background colour. Minimal example.
\documentclass{beamer}
\setbeameroption{show notes}
\setbeamercolor{note page}{bg=white}
% \setbeamertemplate{note page}{plain}
\begin{document}
\begin{frame}
Text\note{note}
\end{frame}
\end{document}