Number theorists have long been interested in the quantitative aspects of the distribution of Galois groups of field extensions. Recently, progress has been realized in counting extensions of function fields over (large enough) finite fields by reducing to characteristic zero, and more specifically to the topology of certain varieties which parametrize extensions. However, these methods apply only to "tame" extensions, where the characteristic does not divide the order of the Galois group. The "wild" case, when the Galois group is a p-group and p is the characteristic of the base field, is very mysterious. In recent work with Fabian Gundlach, we have related extensions of the local function field ?_q((T)) to the solutions to certain equations over the ring W(?_q) of Witt vectors. These equations involve the absolute Frobenius automorphism ? : x ?x?, making them difference equations. Counting extensions (including questions like reduction to characteristic 0, uniformity in the prime p, etc.) is then related to counting points on difference schemes and to the "asymptotic behavior" of the absolute Frobenius automorphism as p grows, thus connecting the initial problem to Hrushovski-Lang-Weil-type estimates. In this talk, I will present these connections and our current results. Efforts will be made towards rephrasing some of our questions in model-theoretic language, including open questions which may benefit from a model-theoretic perspective.