Sound texture perception takes advantage of a hierarchy of time-averaged statistical features of acoustic stimuli, but much remains unclear about how these statistical features are processed along the auditory pathway. Here, we compared the neural representation of sound textures in the inferior colliculus (IC) and auditory cortex (AC) of anesthetized female rats. We recorded responses to texture morph stimuli that gradually add statistical features of increasingly higher complexity. For each texture, several different exemplars were synthesized using different random seeds. An analysis of transient and ongoing multiunit responses showed that the IC units were sensitive to every type of statistical feature, albeit to a varying extent. In contrast, only a small proportion of AC units were overtly sensitive to any statistical features. Differences in texture types explained more of the variance of IC neural responses than did differences in exemplars, indicating a degree of "texture type tuning" in the IC, but the same was, perhaps surprisingly, not the case for AC responses. We also evaluated the accuracy of texture type classification from single-trial population activity and found that IC responses became more informative as more summary statistics were included in the texture morphs, while for AC population responses, classification performance remained consistently very low. These results argue against the idea that AC neurons encode sound type via an overt sensitivity in neural firing rate to fine-grain spectral and temporal statistical features.