Offhand I don't think there is a general statement that can be made that a polarizer warms or cools a scene. The haze we typically see is some combination of Mie and Rayleigh scattering; the Rayleigh will tend to give a bluish look, the Mie more whitish. Most haze I see is bluish white, i.e. a combination of both components. (Not like the coloured haze that people used to see, you know, back in the 60s, but I digress)

Anyway, a polarizer will tend to reduce both components, and what effect you see will depend on the proportion of the components in the first place and the colour temp of the incident light.

Regarding colour temp, the way I think of it, the colour temp of the incident light is mostly determined by upper-atmosphere scattering, i.e. scattering off particles/molecules not between the subject and the lens. But haze is caused by scatter off particles/molecules that are between the subject and the lens. So you can have a warm or cool colour temp, with haze masking that and reducing saturation. Whether you see warming or cooling effect through a polarizer will depend on what the colour temp was for starters.

These are the thoughts that appear logical to me at this hour.