>>4196197[cont] The Complex Part:
Coloured filters block opposing colour. So, warming filter will block blue. Cold filter will block red. Auto white balance and rgb filter arrays mean that camera will compensate any changes by just changing wb. Filter on or off, it won't matter, everything will look the same on first look. But that's just the first look. White balance has limits, pure red, pure blue, pure green, and to a lesser degree, their strong derivatives, cyan, magenta, and yellow, will be composed of clipped channels. Image processors, being RGB, work best when they can use data from all three channels. Having pure colours on the scene, will mean that only one part of photo sites is capturing image, while the other two are doing nothing. Say you're taking a picture of a fire, red channel will be quickly clipped, image processor will figure this, and protect reds from being clipped, but at the price of other two channels. They will be dropped, and record less data. If you use cold filter in front of the lens, and shoot same scene, red channel will still receive the same treatment when wb is set higher, but other two channels will be able to record more. The reverse goes for shooting similar scenes of other pure colours. Benefits, or better said, differences certainly are there, the thing is that you very rarely encounter such scenes. Things get more complex, you have blue sky, all kinds of green, so filter may help in one area, but harm another.
Best to experiment and figure things on your own. It's not hard. Take a photo with a filter, take one without, compare results. Personally, I love shooting warming filters in the winter, when everything is cold and drab. Even when dropping wb way down, and going for the cold look, I find that they offer benefits. On other hand, I think that they are positively ruinous for fall photography.