How to change symbol for footnote in minipage

Change \thempfootnote.

\documentclass{article}
\renewcommand{\thempfootnote}{\arabic{mpfootnote}}
\begin{document}
\begin{minipage}{.5\textwidth}
test this\footnote{abc}
\end{minipage}
\end{document}

If your objective is to just continue with the "global" footnotes through a minipage then look at the example below. It illustrates the two different footnotes and how to use both inside a minipage.

\documentclass{article}
\usepackage{footmisc}% for \footref and \mpfootnotemark
\begin{document}
\noindent\ldots{} main text\footnote{Before minipage} \ldots\par
\fbox{\begin{minipage}{.5\linewidth}
    Footnotes in minipages are numbered using
    lowercase letters\footnote{Inside minipage\label{fn:1}}.\\
    To reuse the previous minipage footnote\footref{fn:1}.\\
    A second minipage footnote\footnote{Again}.\\
    A footnote to use global\footnotemark.\\
    A second global footnote\footnotemark.
\end{minipage}}
%--- Directly after minipage ----------------------------
\addtocounter{footnote}{-1}%
\footnotetext{First global footnote inside minipage}%
\stepcounter{footnote}%
\footnotetext{Second global footnote inside minipage}%
%--------------------------------------------------------
\par
\noindent\ldots{} main text\footnote{After minipage} \ldots\par
\end{document}

If you want all footnotes to be numeric then you must set the mpfootnote counter at the begining of the minipage and reset the footnote counter at the end. Please do not now use \footnotemark inside the minipage, because it will mess up everything.

\documentclass{article}
\begin{document}
\noindent\ldots{} main text\footnote{Before minipage} \ldots\par
\fbox{\begin{minipage}{.5\linewidth}
        \setcounter{mpfootnote}{\value{footnote}}%
        \renewcommand{\thempfootnote}{\arabic{mpfootnote}}%
    Footnotes in minipages\footnote{Inside minipage}.\\
    A second minipage footnote\footnote{Again}.
        \setcounter{footnote}{\value{mpfootnote}}%
\end{minipage}}
\par
\noindent\ldots{} main text\footnote{After minipage} \ldots\par
\end{document}