Another chance arrived for the hosts later in the first half, but Patrick Ziegler could only head over the crossbar after rising highest to meet a Stoppelkamp corner.
Despite an impressive start from Paderborn, it was Koln who should have gone in ahead at the break as Miso Brecko fired over after breaking free from his marker.
Horn was back in action again in the early stages of the second half as he reacted well to push a powerful strike from Elias Kachunga over the crossbar.
Chances continued to be passed up by Paderborn, with Stoppelkamp once again guilty of being wasteful in front of goal as he dragged a shot wide from the edge of the box.
The opportunities would soon dry up, and Koln looked more comfortable late on as the draw was secured.