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 10,000. This has enabled an absolute measurement of the total trap loss cross sections between OH and ND3 at a mean collision energy of 5 K. Due to the dipolar interaction, the total cross section increases upon application of an external polarizing electric field. Cross sections computed from 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 radical and a closed-shell polyatomic molecule.