What was done
The authors begin by noting there is "a strong variability in the timing of seasons in Europe, which is perceived as a signal of a global climate change."  Hence - and in the sound scientific tradition of exploring all possibilities - they investigate an alternative hypothesis, i.e., the idea that earlier onsets of the growing season in Europe are due to warmer winters that are associated with a change in the phase of the North Atlantic Oscillation (NAO), which is a large-scale displacement of air mass between the subarctic and the subtropical regions of the North Atlantic Ocean that is described by an index defined as the difference between the normalized air pressure anomaly at Gibraltar and Reykjavik, Iceland.  To accomplish this task, the authors determined the NAO index dependency of the dates of first leafing and blooming in a number of different plants, the time of pollen season initiation, and the beginning dates of ice breakup on several lakes.

What was learned
In the words of the authors, "spring phenology in Europe is found to be significantly affected by the North Atlantic Oscillation," with high-NAO (warm) winters hastening the occurrence of spring phenophases (budburst and bloom) as well as the production, release, dispersal and transport of pollen.  In fact, they described the relationship between the dependence of the onset of the pollen season on the phases of the NAO as nothing short of "remarkable."  They also found "a significant degree of dependence between NAO and spring cryophenology in northern-central Europe," with high-NAO phases characterized by warm winters leading to earlier dates of ice breakup.

What it means
Although the authors never return to the question of whether recent phenology changes in Europe have anything to do with global warming - probably because they have no basis for doing so - they conclude that changes in the NAO largely explain "both the high- and the low-frequency variability of plant phenology."  And if that can be done, there's not much need to invoke anything else.