Well this is what the FA says….
Their methods of weather prediction remain a secret. The Farmers’ Almanac even gives a pseudonym for its official forecaster, Caleb Weatherbee. The pseudonym has been passed down to forecasters for years.

The FA has stated that its method is an exclusive mathematical and astronomical formula that relies on sunspot activity, tidal action of the moon, planetary position and other factors. It’s the oldest source of consecutively published weather forecasts.

They claim that followers report around an 80 to 85 percent accuracy for its predictions. The publication started in 1818. The editors of the Farmers’ Almanac deny that they use any computer satellite tracking equipment, weather lore or groundhogs.

Some scientific analyses of the FA says that its forecasts have panned out at a rate closer to 50 percent accuracy.
Don’t know that it’s been verified.

Maybe they are Time Travelers! 😎

Of all the methods the Almanac admits to, sunspot activity is the only one scientists say could have some small effect on the weather. “Sunspot activity actually is slightly correlated with Earth's climate,” says Dr. Shane Keating, a physicist with a focus in atmosphere-ocean science.

Basically, the sun's magnetic field switches direction roughly every 11 years. During this period, the number of sunspots varies. Some evidence suggests that periods of fewer sunspots cause at least regional, and possibly global cooling. “However, the effect is fairly small compared with the natural variability of Earth's climate,” Keating says. And if there is an effect, it would be seen in terms of years or decades, not seasons, say NWS meteorologists. “Sunspot activity alone cannot accurately predict whether one's summer will be hot, winter will be cold, etc.”

https://www.mentalfloss.com/article/57554/how-does-farmers-almanac-work

I thought because they follow astrology. :)

follow the stars