Global warming is predicted to cause substantial habitat rearrangements, with the most severe effects expected to occur in high-latitude biomes. However, one major uncertainty is whether species will be able to shift their ranges to keep pace with climate-driven environmental changes. Many recent studies on mammals have shown that past range contractions have been associated with local extinctions rather than survival by habitat tracking. Here, we have used an interdisciplinary approach that combines ancient DNA techniques, coalescent simulations and species distribution modelling, to investigate how two common cold-adapted bird species, willow and rock ptarmigan (Lagopus lagopus and Lagopus muta), respond to long-term climate warming. Contrary to previous findings in mammals, we demonstrate a genetic continuity in Europe over the last 20 millennia. Results from back-casted species distribution models suggest that this continuity may have been facilitated by uninterrupted habitat availability and potentially also the greater dispersal ability of birds. However, our predictions show that in the near future, some isolated regions will have little suitable habitat left, implying a future decrease in local populations at a scale unprecedented since the last glacial maximum.