It is unclear how regional and global climate variability depends on the mean state of the climate system, and whether the sensitivity to natural forcing from volcanic eruptions and solar variations is different. Investigating recent volcanic eruptions, well covered by the instrumental record, can give detailed insights into the response of the system close to its present-day state. The paleoclimate record is crucial to establish the role of natural forcing in generating climate variability in states that are very different from today. It is clear that small and large volcanic eruptions occurred throughout the last Glacial cycle and the Holocene, although possibly at a lower rate than during the last millennium. Yet, most climate model experiments for these periods are performed with constant solar and no volcanic forcing. This biases model estimates in model-data comparisons for past climate variability. Here we present first results from an ensemble of long (>1000a) paleoclimate model experiments. Simulations for the Last Glacial Maximum, the mid-Holocene, the Preindustrial and the past millennium were performed under PMIP3 boundary conditions, and with/without solar variability and volcanic forcing. We evaluate, to what extent regional and global climate impacts of this natural forcing is dependent on the mean climate state. As the model includes water isotope diagnostics, we further determine to what extent the variability is consistent with the paleoclimate proxy evidence from ice cores.