How to set superscript footnote mark in the text body but normalsized in the foot?

Use the scrextend package (part of KOMA-script) to customize footnotes. See section 3.14 of the documentation of KOMA-script for details about the \deffootnote macro.

\documentclass{article}

\usepackage{scrextend}
\deffootnote{0em}{1.6em}{\thefootnotemark.\enskip}

\usepackage[english]{babel}
\usepackage{blindtext}

\begin{document}

\blindtext\footnote{\blindtext}

\end{document}

I already had a solution for this problem, which I managed to come up by trial and error... I just didn't know if it was the best way to do it:

\makeatletter
  \renewcommand\@makefntext[1]{%
  \hspace*{-2em}
  \parindent 0em
  \noindent
  \hb@xt@ 1.8em{\hss %  There's the option of putting \hss before
  \@thefnmark. }%       or after \@thefnmark, aligning the footnote
  #1}%                  marks to the right or to the left, respectively
\makeatother

I tried to look at the definition of \deffootnote in scrextend.sty, but it seems to be much more complicated than that...

Anyway, the solution proposed by @lockstep is much simpler than this, although this one might be useful for class authors. Hope it helps.

This is a TeX approach, with doesn't need a package. I use it always. Maybe the code can be improved:

\documentclass{article}

\makeatletter
\newlength{\fnBreite}
\renewcommand{\@makefntext}[1]{%
  \settowidth{\fnBreite}{\footnotesize\@thefnmark.i}
  \protect\footnotesize\upshape%
  \setlength{\@tempdima}{\columnwidth}\addtolength{\@tempdima}{-\fnBreite}%
  \makebox[\fnBreite][l]{\@thefnmark.\phantom{}}%
  \parbox[t]{\@tempdima}{\everypar{\hspace*{1em}}\hspace*{-1em}\upshape#1}}
\makeatother

\usepackage[english]{babel}
\usepackage{blindtext}

\begin{document}

\blindtext\footnote{\blindtext}

\end{document}