Small Cover is an $n$-dimensional manifold endowed with
a $\mathbf{Z}_2^n$ action whose orbit space is
a simple convex polytope $P$.
It is known that a small cover over $P$ is characterized
by a coloring of $P$ which satisfies a certain condition.
In this paper we shall investigate the topology of
small covers by the coloring theory in combinatorics.
We shall first give an orientability condition for a small cover.
In case $n=3$, an orientable small cover corresponds to
a four colored polytope.
The four color theorem implies the existence of orientable
small cover over every simple convex $3$-polytope.
Moreover we shall show the existence of non-orientable
small cover over every simple convex $3$-polytope, except the
$3$-simplex.