As an ("amateur") entomologist, just gonna say -
The forecast thing is a myth, but I'm sure most of you know that.
Solid black "woolly bears" are actually a different species, mainly just meaning you have more or less of their desired foodsource or they are more or less being controlled in population. Out here I rarely ever get any because I don't have the proper plants for it, however just a mile down the road there's quite a few.
Chestnut brown, no black - Again a different species.
Also, colors change through their life stages. Some common species such as the Virginian Tiger Moth actually start out white, then turn golden, then brown, and if you catch them just before pupation they're nearly black.
Isabella Tigers (common "woolly bear") actually often are further from or towards hibernation or pupation based on their amount of brown. Means little to nothing on weather.
Often people just catch them at different stages, and sometimes if you see a trend of more or less brown vs black, you're seeing a trend of a hatch-date.