  In this paper, we prove a lower bound for the Galois orbits of a pure special
subvariety in a general mixed Shimura variety. For special subvarieties that
are not pure, we propose the notion of test invariants as a substitute for the
lower bound estimation, and prove the bounded equidistribution for sequences of
special subvarieties with uniformly bounded test invariants in a given mixed
Shimura variety. Both the estimation and the bounded equidistribution rely on
the Generalized Riemann Hypothesis for CM fields, similar to the pure case
treated by E. Ullmo and A. Yafaev as part of the ergodic-Galois alternative for
the Andr\'e-Oort conjecture for pure Shimura varieties.
