In this analysis we illustrate how the relatively new emission mechanism known as spinning dust can be used to characterize dust grains in the interstellar medium. We demonstrate this by using spinning dust emission observations to constrain the abundance of very small dust grains (a $lesssim$ 10nm) in a sample of Galactic cold cores. Using the physical properties of the cores in our sample as inputs to a spinning dust model, we predict the expected level of emission at a wavelength of 1cm for four different very small dust grain abundances, which we constrain by comparing to 1cm CARMA observations. For all of our cores we find a depletion of very small grains, which we suggest is due to the process of grain growth. This work represents the first time that spinning dust emission has been used to constrain the physical properties of interstellar dust grains.