I have seen similar problems here before, but they mainly asked about how to get the coloring right for the whole document, but I just want to change the color for specific footnotes. I think a definition of a new command is required, but I somehow do not get it to work.
Perhaps you may help me.
\documentclass[11pt, oneside, a4paper]{article}
\usepackage{xcolor}
\usepackage[bottom]{footmisc}
\begin{document}
\color{gray!80}
Here is some text with a footnote\footnote{... in which both number related
to this footnote and also its text should be red!}
Here is some more text with a footnote\footnote{... in which both number
related to this footnote and also its text should be black!}
\end{document}