  The evolution of a turbulent tangle of quantum vortices in presence of
finite-size active particles is studied by means of numerical simulations of
the Gross-Pitaevskii equation. Particles are modeled as potentials depleting
the superfluid and described with classical degrees of freedom following a
Newtonian dynamics. It is shown that particles do not modify the building-up
and the decay of the superfluid Kolmogorov turbulent regime. It is observed
that almost the totality of particles remains trapped inside quantum vortices,
although they are occasionally detached and recaptured. The statistics of this
process are presented and discussed. The particle Lagrangian dynamics is also
studied. At large time scales, the velocity spectrum of particles is
reminiscent of a classical Lagrangian turbulent behavior. At time-scales faster
than the turnover time associated to the mean inter-vortex distance, the
particle motion is dominated by oscillations due to Magnus effect. For light
particles a non-classical scaling of the spectrum arises. The particle velocity
and acceleration probability distribution functions are then studied. The
decorrelation time of the particle acceleration is found to be shorter than in
classical fluids, and related to the Magnus force experienced by the trapped
particles.
