The "headers" are created using the bibmacro entryhead:full (or entryhead:name, depending on the value passed to entryhead).
In order to also colour in the entry head we just apply the code in \AtEveryBibitem to entryhead:full:
\renewbibmacro*{entryhead:full}{%
\ifcategory{important}
{\bfseries\color{impentry}}
{}
\printnames[labelname][-1]{labelname}%
\setunit*{\addcolon\space}%
\printfield{labeltitle}}
This is analogous for entryhead:name:
\makeatletter
\newbibmacro*{entryhead:name}{%
\ifcategory{important}
{\bfseries\color{impentry}}
{}
\ifnameundef{labelname}
{\printfield{labeltitle}}
{\printnames[labelname]{labelname}}%
\savefield{fullhash}{\bbx@lasthash}}
\makeatother
If you want to keep the colouring more local (don't colour the entry key) we can do that with a bit of group action:
\renewbibmacro*{entryhead:full}{%
\begingroup
\ifcategory{important}
{\bfseries\color{impentry}}
{}
\printnames[labelname][-1]{labelname}%
\setunit*{\addcolon\space}%
\printfield{labeltitle}
\endgroup}
MWE
\documentclass[12pt]{article}
\usepackage[T1]{fontenc}
\usepackage[style=reading]{biblatex}
\addbibresource{biblatex-examples.bib}
%% Highlight entries
\usepackage[svgnames]{xcolor}
\DeclareBibliographyCategory{important}
% the colour definition
\colorlet{impentry}{Maroon}% let 'impentry' = Maroon
% Inform biblatex that all books in the 'important' category deserve
% special treatment, while all others do not
\AtEveryBibitem{%
\ifcategory{important}%
{\bfseries\color{impentry}}%
{}%
}
% Add books to 'important' category in preamble
\addtocategory{important}{%
cicero,
}
\renewbibmacro*{entryhead:full}{%
\ifcategory{important}
{\bfseries\color{impentry}}
{}
\printnames[labelname][-1]{labelname}%
\setunit*{\addcolon\space}%
\printfield{labeltitle}}
\begin{document}
\nocite{wilde,cicero}
\printbibliography
\end{document}

If you also want to colour in the horizontal rule, it is probably better to modify another macro (that is, you do not have to apply the customisations to entryhead:full above)
\makeatletter
\def\bbx@item@full{%
\begingroup
\ifcategory{important}
{\color{impentry}}
{}
\itemsep2\bibitemsep
\@itempenalty\z@
\item\relax
\begingroup
\samepage\bfseries
\def\finentrypunct{\strut}%
\usebibmacro{entryhead:full}%
\ifbool{bbx:entrykey}
{\def\newblockpunct{%
\nobreak\hskip\z@skip\strut
\hfill\penalty100\hskip1em\relax
\hbox{}\nobreak\hfill\strut}%
\def\finentrypunct{%
\parfillskip\z@\finalhyphendemerits\z@
\par\nobreak}%
\newblock
\printfield{entrykey}}
{}%
\finentry
\endgroup
\hrule height 1.25pt\relax
\itemsep\bibitemsep
\@itempenalty\@M
\item\strut
\@itempenalty\z@
\endgroup}
\makeatother
MWE
\documentclass[12pt]{article}
\usepackage[T1]{fontenc}
\usepackage[style=reading]{biblatex}
\addbibresource{biblatex-examples.bib}
%% Highlight entries
\usepackage[svgnames]{xcolor}
\DeclareBibliographyCategory{important}
% the colour definition
\colorlet{impentry}{Maroon}% let 'impentry' = Maroon
% Inform biblatex that all books in the 'important' category deserve
% special treatment, while all others do not
%\AtEveryBibitem{%
% \ifcategory{important}%
% {\bfseries\color{impentry}}%
% {}%
% }
% Add books to 'important' category in preamble
\addtocategory{important}{%
cicero,
}
\AtEveryBibitem{%
\ifcategory{important}%
{\bfseries\color{impentry}}%
{}%
}
\makeatletter
\def\bbx@item@full{%
\begingroup
\ifcategory{important}
{\color{impentry}}
{}
\itemsep2\bibitemsep
\@itempenalty\z@
\item\relax
\begingroup
\samepage\bfseries
\def\finentrypunct{\strut}%
\usebibmacro{entryhead:full}%
\ifbool{bbx:entrykey}
{\def\newblockpunct{%
\nobreak\hskip\z@skip\strut
\hfill\penalty100\hskip1em\relax
\hbox{}\nobreak\hfill\strut}%
\def\finentrypunct{%
\parfillskip\z@\finalhyphendemerits\z@
\par\nobreak}%
\newblock
\printfield{entrykey}}
{}%
\finentry
\endgroup
\hrule height 1.25pt\relax
\itemsep\bibitemsep
\@itempenalty\@M
\item\strut
\@itempenalty\z@
\endgroup}
\makeatother
\begin{document}
\nocite{wilde,cicero}
\printbibliography
\end{document}