Extreme weather events have significant consequences, dominating the impact of climate on society, but occur with small probabilities that are inherently difficult to compute. A rare event with a 100year return period takes, on average, 100 years of simulation time to appear just once. Computational constraints limit the resolution of models used for such long integrations, but high resolution is necessary to resolve extreme event dynamics. We demonstrate a method to exploit short-term forecasts from a high-fidelity weather model and lasting only weeks rather than centuries, to estimate the long-term climatological statistics of rare events. Using only two decades of forecast data, we are able to robustly estimate return times on the centennial scale. We use the mathematical framework of transition path theory to compute the rate and seasonal distribution of sudden stratospheric warming (SSW) events of varying intensity. We find SSW rates consistent with those derived from reanalysis data, but with greater precision. Our method performs well even with simple feature spaces of moderate dimension, and holds potential for assessing extreme events beyond SSW, including heat waves and floods.