Recent research has established a statistical link between North American cold spells (CS) and concurrent wet or windy extremes in Europe. Here, we investigate whether such a link can be related to changes in the characteristics of North Atlantic extratropical cyclones (hereafter cyclones). Despite large regions of anomalous baroclinicity during periods of North American CS, the number of cyclones across the North Atlantic as a whole is not significantly above climatology. However, we observe rates of explosive cyclogenesis significantly above climatology. We further find that CS over different North American regions are associated with large-scale atmospheric configurations displaying a strenghtened jet stream in the vicinity of the CS and different upper-level wind anomalies in the East Atlantic. These, in turn, modulate the regional distributions and characteristics of cyclones in the North Atlantic and Europe. We compute a fixed-radius cyclone footprint which we use to associate extreme precipitation and wind occurrences to individual cyclones. For eastern Canada CS, the North Atlantic jet extends over Northern Europe, resulting in a heightened numbers of cyclones for the British Isles and Scandinavia, while France, the British Isles, Northern Europe and Scandinavia all experience more intense cyclones. The British Isles consistently experience wind extremes associated with cyclones during east Canada CS. For central Canada CS, the jet is displaced poleward and only partly extends over Europe, resulting in an above average cyclone density in the eastern Atlantic and a higher number of cyclones affecting Iberia only. Iberia consistently experiences precipitation extremes associated with the cyclones during central Canada CS. For eastern United States CS, the jet is displaced equatorward and extends over Southern Europe, with a significantly heightened number of cyclones affecting Iberia and France. Iberia experiences wind extremes associated with the cyclones during eastern United States CS. Our results provide a dynamical explanation for previous statistical findings on the concurrence of North American CS and wet or windy extremes over Europe.