Weather predictions are mathematically impossible beyond about 3 weeks. Even if you have a supercomputer that has the compute equal to about 100 suns worth of energy per second, even if you have a database that knows the position of every air molecule, the nature of complex systems is that tiny tiny differences in initial conditions can result in completely opposite weather situations. This is why we can't predict the weather in 3 weeks time. But we can predict the climate in 50 years time.
It is simply the nature of complex systems like weather. The lifetime of low or high pressure areas is usually 3 to 4 days. So after that period, new ones appear, which you can still predict, but with some error. Then once those go and you get the third generation, the error margins become quite high. And by the 4th cycle, they could be anywhere. And you literally have no idea where the low-pressure areas and anticyclones would be. The math would simply state they are equally probably to be at almost any position.
It is key to realize that this is an inherit property of these systems. And not an issue of lack of understanding or limited computational power. We can still push predictions to be more accurate, sure. But it becomes exponentially harder to predict 1 more day ahead. Until you fall off a cliff and no amount of knowledge of compute can get you any improvement. Where that point is for weather is still up to debate.
So when people say they can predict that a winter will be mild or cold, usually they talk about 2 to 4 months into the future, it is pure pseudoscience. Sure, there are some multi-year cycles like El Nino that you can predict and that can affect weather. But in the end the local weather will determine if your winter is cold or not.