Kurt,

A UV/Haze filter will affect blue, causing attenuation of those wavelengths. Given that, the white balance as seen Through The Lens (TTL) is already "offset" to less blue. That leaves the camera some less latitude to set a white balance automatically for the way your eyes see a scene. A skylight filter is for high-altitude photography, an environment which tends to have even more predominant blue light. Again, such a filter would attenuate blue wavelengths, so that means your camera could not using all of the input seen TTL.

OTOH, you may have an aesthetically favorable result from taking out some/excessive blue out, or you may not. I would say that depends on the light (such as time of day), the scene, whether you're using fill-flash, and your camera's white balance algorithm. Perhaps other factors as well.

If you don't want automatic processing, can usually preset the camera for a white balance that you prefer though, matching it to the dominant light for your scene. In other cases, like strong mixed light (daylight and interior lighting, for example), the camera's automatic white balance (AWB) may well perform better than a preset white balance, esp. because lenses do tend to collect light in a directional way, whereas our eyes are more "wideangle."

But white balance is really sometimes a compromise, as "true" balance becomes impossible. The camera's optical transfer function by wavelength is not fully linear, nor is it the same as human vision. A classic case for the stage is photographing a red or green velvet or felt material ... they always go dark, or shift in color. You can look through the viewfinder and see a different color than what your eyes see! The fabrics are actually miniature light traps, which is an effect caused through numerous convolutions of the material. Another case that happened to me was photographing speakers at a podium on a stage (and full hall, actually) that was completely ringed in blue light, whereas the stage was lighted with bright yellow spotlights ... in that chromaticity situation, there is no possible white balance. Taking away blue adds yellow, and vice versa.

There is another way to manage white balance though. If you shoot in camera raw, the white balance can be set later, and you don't really need to worry about it. The AWB, or a manual one, are only settings for rendering a JPEG photo out of your camera. You can do that yourself, or obtain higher resolution color output (such as via TIFF output files created from camera raw), instead of having the camera generate toned JPEGs for you automatically.

I should be very clear that camera raw (along with relevant software) gives you the latitude to manage where the white and black point is for each photo, but in no way does it make up for the effects inherent in recording strong mixed light in a scene. For a really important photo, if it was taken in strongly mixed light (or you lost too much blue because of 1A filter), you may have to do work with an image editor. For example, by making separate layers, which are masked and then toned separately, to get the "look" you may have wanted for that photo.

Blessings and Light,
M