  We prove a uniform version of non-Archimedean Yomdin-Gromov parametrizations
in a definable context with algebraic Skolem functions in the residue field.
The parametrization result allows us to bound the number of F_q[t]-points of
bounded degrees of algebraic varieties, uniformly in the cardinality q of the
finite field F_q and the degree, generalizing work by Sedunova for fixed q. We
also deduce a uniform non-Archimedean Pila-Wilkie theorem, generalizing work by
Cluckers-Comte-Loeser.
