  The use of High Purity Germanium detectors operated in ionization mode at
cryogenic temperatures is investigated as an external background mitigation
solution for bolometers used in rare-event search experiments. A simple
experimental setup with very partial coverage, running a 52-g
$\mathrm{Li_2WO_4}$ bolometer sandwiched in-between two 2-cm thick High Purity
Germanium cylindrical detectors in a dry cryostat, shows promising rejection to
environmental gammas and atmospheric muons backgrounds. The acquired data are
used together with a Monte Carlo simulation of the setup to extract the main
contributions to the external backgrounds expected in an above ground
experiment, such as e.g.~current and future experimental efforts targeting the
detection of coherent elastic neutrino-nucleus scattering at reactor
facilities. Based on all these results, a $\mathrm{4\pi}$ coverage similar veto
system achieving a $\mathcal{O}$(10 keV) energy threshold is expected to
achieve a $\mathrm{\gtrsim}$ 70 \% and a $\mathrm{\gtrsim}$ 97 \% rejection
power for gamma-like and muon-like events, respectively.
