We present a newly developed time-dependent three-dimensional multi-zone hadronic blazar emission model. By coupling a Fokker-Planck based lepto-hadronic particle evolution code 3DHad with a polarization-dependent radiation transfer code, 3DPol, we are able to study the time-dependent radiation and polarization signatures of a hadronic blazar model for the first time. Our current code is limited to parameter regimes in which the hadronic $gamma$-ray output is dominated by proton synchrotron emission, neglecting pion production. Our results demonstrate that the time-dependent flux and polarization signatures are generally dominated by the relation between the synchrotron cooling and the light crossing time scale, which is largely independent of the exact model parameters. We find that unlike the low-energy polarization signatures, which can vary rapidly in time, the high-energy polarization signatures appear stable. As a result, future high-energy polarimeters may be able to distinguish such signatures from the lower and more rapidly variable polarization signatures expected in leptonic models.