  Einstein-Podolski-Rosen steering is a form of quantum correlation exhibiting
an intrinsic asymmetry between two entangled systems. In this paper, we propose
a scheme for examining dynamical Gaussian quantum steering of two mixed
mechanical modes. For this, we use two spatially separated optomechanical
cavities fed by squeezed light. We work in the resolved sideband regime.
Limiting to the adiabatic regime, we show that it is possible to generate
dynamical Gaussian steering via a quantum fluctuations transfer from squeezed
light to the mechanical modes. By an appropriate choice of the environmental
parameters, one-way steering can be observed in different scenarios. Finally,
comparing with entanglement - quantified by the Gaussian R\'enyi-2 entropy-, we
show that Gaussian steering is strongly sensitive to the thermal effects and
always upper bounded by entanglement degree.
