Many plants require vernalization, or winter chilling, to promote flowering in the spring. In Arabidopsis thaliana, vernalization is a quantitative response to both the duration and intensity of cold, and is a classic example of epigenetic memory in plants. Here we tested if the vernalization response of A. thaliana was also quantitatively related to the timing of the cold during development – e.g., if vernalization was less effective in plants that germinate and grow considerably before the onset of winter – an ecologically relevant parameter in locations with uncertain fall rainfall. We measured the effect of different onset-dates of a simulated winter on gene expression responses of vernalization-pathway genes in leaves that developed before or after the onset of cold temperatures. We observed different reactions to cold in different genes in the pathway, and a clear spatial pattern of vernalization responses across leaves – suggesting additional complexity to the vernalization response in this species.  Based on these data, we propose a two-level digital model for the quantitative memory of vernalization: that the length of the cold is recorded digitally at the level of cells, as was previously known, and that the timing of the cold is recorded digitally in the number of vernalized leaves. This spatial encoding of temporal memory provides novel insight into the mechanisms underlying long-term, quantitative, plant responses to dynamic environments that may be applicable to other systems including crops.