Understanding the effects of past climatic fluctuations on the distribution and population-size dynamics of cold-adapted species is essential for predicting their responses to ongoing global climate change. In spite of the heterogeneity of cold-adapted species, two main contrasting hypotheses have been proposed to explain their responses to Late Quaternary glacial cycles, namely, the interglacial contraction versus the interglacial expansion hypotheses. Here, we use the cold-adapted plant Primula farinosa to test two demographic models under each of the two alternative hypotheses and a fifth, null model. We first approximate the time and extent of demographic contractions and expansions during the Late Quaternary by projecting species distribution models across the last 72 ka. We also generate genome-wide sequence data using a Reduced Representation Library approach to reconstruct the spatial structure, genetic diversity, and phylogenetic relationships of lineages within P. farinosa. Finally, by integrating the results of climatic and genomic analyses in an Approximate Bayesian Computation framework, we propose the most likely model for the extent and direction of population-size changes in $P$. farinosa through the Late Quaternary. Our results support the interglacial expansion of $P$. farinosa, differing from the prevailing paradigm that the observed distribution of cold-adapted species currently fragmented in high altitude and latitude regions reflects the consequences of postglacial contraction processes.