Extratropical precipitation trends are strongly affected by changes in large-scale circulation, but the relevant dynamic signals are often difficult to isolate in climate models. Here, we introduce a low-dimensional framework that reconstructs Northern Hemisphere winter precipitation trends from leading modes of 500-hPa geopotential-height variability. The framework decomposes circulation variability into transient, stationary, and interaction components, and links their EOF modes to precipitation using ERA5 and CMIP6 historical and SSP5-8.5 simulations. In ERA5, the leading circulation modes reproduce much of the observed precipitation redistribution, with drying in the subtropics and wetting in the midlatitudes. The transient storm-track component dominates the reconstruction, with shift and sharpening modes accounting for most of the circulation-linked precipitation trend. CMIP6 models capture the broad meridional structure of this response but underestimate its amplitude. The weak multi-model mean response results from large intermodel spread and sign cancellation in the pulsing and shift modes, while the sharpening mode remains more coherent across models. Under SSP5-8.5, circulation-induced precipitation trends become weaker relative to total precipitation trends, consistent with an increasing role of thermodynamic moistening. Nevertheless, the spatial structure of precipitation change remains strongly tied to storm-track variability. These results suggest that uncertainty in future extratropical precipitation redistribution depends not only on the magnitude of warming but also on how models represent the modal structure of storm-track change and its coupling to precipitation.