The year when King Charles the twelfth of Sweden was advancing towards Moscow during the great Northern War was exceptionally cold. This winter was not calculated by Sweden and Charles had to escape to the Ukraine and Ottoman Empire to resupply. What were the causes of the Great Frost of 1709 and was it ever predicted?
Per the wikipedia page I edited into your answer, the causes were unknown, and it is still inexplicable using modern climate models, so even if someone had predicted it it would not have been based on anything other than guesswork.
This winter event has drawn the attention of modern-day climatologists in the European Union's Millennium Project because they are presently unable to correlate the known causes of cold weather in Europe today with weather patterns documented in 1709. According to Dennis Wheeler, a climatologist at the University of Sunderland: "Something unusual seems to have been happening".
Modern climate models do not appear to be entirely effective for explaining the climate of 1709.
Supporting sources from the wiki pages:
Adding to this, intuitively it makes sense to assume that the cause would have been some kind of polar vortex coming down onto Europe or its whereabouts. Usually this introduces pockets of cold coming from Siberia into Europe brought by winds from the (North-)East, as happened during the nastier winters we had in the past few years. The very odd part about the 1709 winter is that winds were reportedly coming from the West and the South.