How does the Farmers Almanac predict the weather almost a year before it happens?
Seems to me that your selective memory is at work – recalling the times it was accurate and forgetting about those it wasn’t. Some skill above climatology *may* be shown for the general seasonal trends, but it is certainly impossible to predict weather for specific days a year in advance. The way to test them of course is with verifications. For example, choose a region and use the observed data in it for each month to see how accurate their forecast temperature anomalies are. Do the same thing qualitatively for the daily forecasts (have to develop some accuracy criteria – e.g., if the forecast says cloudy & cool for a 4 day period, what type of weather would be considered accurate). Compare the latter with the zone forecasts from the National Weather Service. That takes quite a bit of effort if done properly, but sure beats an opinion based on a general notion.
