Cryogenic optomechanical cavities fabricated from silicon are promising candidates for quantum information applications and platforms to study mesoscale quantum physics. However, the low temperature behaviour of these devices remains shrouded in mystery. To elucidate this, we have designed and built an optomechanical coupling apparatus inside of a dilution refrigerator, which we use to study on-chip silicon optical microdisks coupled to nanomechanical beams. Using an optomechanically mediated thermal ringdown technique, we measure the dissipation in a half-ring resonator between 10 mK to 10 K, and attribute it to two-level system defects embedded within the one-dimensional geometry of the device. Modifying the standard tunneling model to describe this damping mechanism, we determine the density of states and deformation potentials of these two-level system ensembles, postulating that they originate from surface defects. We also study a low temperature photothermal backaction force observed in our devices that acts to suppress conventional radiation-pressure effects. Using a photothermal optomechanical model, we find that this interaction can, in principle, be exploited to cool our resonator's motion into its ground state. Finally, we use a master equation approach to assess the feasibility of using our device geometry to perform nonlinear optomechanical measurements of quantized mechanical energy. In doing so, we set an upper limit on the allowable linear coupling strength of the system, which is significantly less stringent than the single-photon strong coupling regime required in previously studied optomechanical cavities.