\documentclass[headheight=19pt]{scrartcl}
%------------------------------------------------------------------------------
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage[ngerman]{babel}
\usepackage{amsmath}
\usepackage[thmmarks,amsmath]{ntheorem}
\usepackage{multicol}
\usepackage{enumerate}
%-------------------------------------------------------------------------------
\theoremstyle{break}
\theoremheaderfont{\sffamily\small\bfseries}
\theorembodyfont{\normalfont\small}
\theoremindent1em
\newtheorem{Bei}{Beispiel}
%------------------------------------------------
\begin{document}
\begin{Bei}
Mit Text verrutscht nichts.
\begin{multicols}{3}
\begin{enumerate}[a)]
\item $1$
\item $2$
\item $3$
\end{enumerate}
\end{multicols}
\end{Bei}
\begin{Bei}\leavevmode\vspace{-\baselineskip}
\begin{multicols}{3}
\begin{enumerate}[a)]
\item $1+1$
\item $2+2$
\item $3+3$
\end{enumerate}
\end{multicols}
\end{Bei}
\end{document}