We investigate spin dynamics in antiferromagnetic multiferroic TbMnO3 using optical-pump, terahertz (THz)-probe spectroscopy. Photoexcitation results in a broadband THz transmission change, with an onset time of 25 ps at 10 K that becomes faster at higher temperatures. We attribute this time constant to spin-lattice thermalization. The excellent agreement between our measurements and previous ultrafast resonant x-ray diffraction measurements on the same material confirms that our THz pulse directly probes spin order. Furthermore, the presence of a pump-probe signal above the magnetic ordering temperatures suggests that, unlike resonant x-ray probing, THz transmission is sensitive to the dynamics of short-range spin order, which is known to be of importance in spin-spiral multiferroics like TbMnO3.