Natural forcing from solar and volcanic activity contributes significantly to climate variability. The post-eruption cooling of strong volcanic eruptions was hypothesized to have led to millennial-scale variability in the Glacial and to be weakened in warmer climate states. The underlying question is whether the climatic response to natural forcing is state-dependent. Here, we quantify the response to natural forcing under Last Glacial and Pre-Industrial conditions in an ensemble of climate model simulations. We evaluate internal and forced variability on annual to multicentennial scales. The global temperature response reveals no state dependency. Findings on the ability of models to simulate past variability could therefore translate to future climates. Small local differences result mainly from state-dependent sea ice changes. Variability in forced simulations matches paleoclimate reconstructions significantly better than in unforced scenarios. Considering natural forcing is therefore important for model-data comparison and future projections.