I can’t say that The Farmer’s Almanac has a strong statistical association with predictive weather patterns, but NOAA isn’t much better.
I think the FA is well regarded, though their predictions are of the broad brush variety. They predict forecasts such as hotter-colder-wetter-dryer, etc for 16 regional areas of the USA and they are usually right.
Like the article says, they have used predictive methods such as planetary positions, sunspots and lunar cycles for 200 years. I guess that can work if you know what to look for.