We present the first 3.8 mum image of the dusty ring surrounding the young binary system GG Tau, obtained with the W. M. Keck II 10 m telescope's adaptive optics system. This is the longest wavelength at which the ring has been detected in scattered light so far, allowing a multiwavelength analysis of the scattering properties of the dust grains present in this protoplanetary disk in combination with previous, shorter wavelength, Hubble Space Telescope images. We find that the scattering phase function of the dust grains in the disk is only weakly dependent on the wavelength. This is inconsistent with dust models inferred from observations of the interstellar medium or dense molecular clouds. In particular, the strongly forward-throwing scattering phase function observed at 3.8 mum implies a significant increase in the population of large (greater than or similar to1 mum) grains, which provides direct evidence for grain growth in the ring. However, the grain size distribution required to match the 3.8 mum image of the ring is incompatible with its published 1 mum polarization map, implying that the dust population is not uniform throughout the ring. We also show that our 3.8 mum scattered light image probes a deeper layer of the ring than previous shorter wavelength images, as demonstrated by a shift in the location of the inner edge of the disk's scattered light distribution between 1 and 3.8 mum. We therefore propose a stratified structure for the ring in which the surface layers, located similar to 50 AU above the ring midplane, contain dust grains that are very similar to those found in dense molecular clouds, while the region of the ring located similar to 25 AU from the midplane contains significantly larger grains. This stratified structure is likely the result of vertical dust settling and/or preferred grain growth in the densest parts of the ring.