The conserved Polycomb repressive complex 2 (PRC2) generates trimethylation of histone 3 lysine 27 (H3K27me3), a modification associated with stable epigenetic silencing. Much is known about PRC2-induced silencing but key questions remain concerning its nucleation and stability. Vernalization, the perception and memory of winter in plants, is a classic epigenetic process that, in Arabidopsis, involves PRC2-based silencing of the floral repressor FLC. The slow dynamics of vernalization, taking place over weeks in the cold, generate a level of stable silencing of FLC in the subsequent warm that depends quantitatively on the length of the prior cold. These features make vernalization an ideal experimental system to investigate both the maintenance of epigenetic states and the switching between them. Here, using mathematical modelling, chromatin immunoprecipitation and an FLC:GUS reporter assay, we show that the quantitative nature of vernalization is generated by H3K27me3-mediated FLC silencing in the warm in a subpopulation of cells whose number depends on the length of the prior cold. During the cold, H3K27me3 levels progressively increase at a tightly localized nucleation region within FLC. At the end of the cold, numerical simulations predict that such a nucleation region is capable of switching the bistable epigenetic state of an individual locus, with the probability of overall FLC coverage by silencing H3K27me3 marks depending on the length of cold exposure. Thus, the model predicts a bistable pattern of FLC gene expression in individual cells, a prediction we verify using the FLC:GUS reporter system. Our proposed switching mechanism, involving the local nucleation of an opposing histone modification, is likely to be widely relevant in epigenetic reprogramming.