We develop, evaluate, and apply "SynthETC," a statistical-stochastic model of winter extra-tropical cyclones (ETCs) over eastern North America. SynthETC simulates the life cycle of ETCs from formation to termination, and it can be used to estimate the probability of extreme ETC events beyond the historical record. Two modes of climate variability are used as independent covariates: El Niño/Southern Oscillation (ENSO) Niño3.4 and the monthly North Atlantic Oscillation (NAO). We use SynthETC to estimate the annual occurrence rate over sites in eastern North America of intense ETC passage in different ENSO and NAO states. Positive NAO is associated with increased rates over the North Atlantic, while negative NAO is associated with decreased rates over the North Atlantic and increased rates over northern Quebec. Positive ENSO is associated with decreased rates over the North Atlantic, Ontario, and the Canadian Maritime, while negative ENSO is associated with increased rates over those regions, as well as the Great Lakes region.