A non-homogeneous hidden Markov model (NHMM) is applied for downscaling atmospheric synoptic patterns to winter multi-site daily precipitation amounts. The implemented NHMM assumes precipitation to be conditional on a hidden weather state that follows a Markov chain, whose transition probabilities depend on current atmospheric information. The gridded atmospheric fields are summarized through the singular value decomposition (SVD) technique. SVD is applied to geopotential height and relative humidity at several pressure levels, to identify their principal spatial patterns co-varying with precipitation. We assume the common hidden weather state process to completely account for the temporal structure of precipitation. Given the current weather state, the multivariate probability distribution of precipitation occurrences is approximated using a Chow-Liu tree dependence structure, involving products of bivariate distributions. Conditional on the weather state, precipitation amounts are modelled separately at each gauge as independent gamma-distributed random variables. This modelling approach is applied to 51 precipitation gauges in Denmark and southern Sweden for the period 1981-2003. The downscaling model produces robust predictions of data statistics, such as expected precipitation amounts and spell duration distributions. Moreover, the model-defined weather states show a satisfactory degree of physical consistency.