  We present the first experimental observation of cold collisions between two
different species of neutral polar molecules, each prepared in a single
internal quantum state. Combining for the first time the techniques of Stark
deceleration, magnetic trapping, and cryogenic buffer gas cooling allows the
enhancement of molecular interaction time by 10$^5$. This has enabled an
absolute measurement of the total trap loss cross sections between OH and
ND$_3$ at a mean collision energy of 3.6 cm$^{-1}$ (5 K). Due to the dipolar
interaction, the total cross section increases upon application of an external
polarizing electric field. Cross sections computed from \emph{ab initio}
potential energy surfaces are in excellent agreement with the measured value at
zero external electric field. The theory presented here represents the first
such analysis of collisions between a $^2\Pi$ radical and a closed-shell
polyatomic molecule.
