Yes! This is something I've been trying to document properly for about three years now. At a location in Worcestershire we investigated last autumn, the cold spot moved in almost a perfect L-shape through two rooms, same route every single time we tracked it. We mapped it on four separate visits and the path barely deviated.
My working theory is that cold spots follow whatever residual energy pathway got established during the original event - like a groove worn into the fabric of the place. Some investigators call this a "trauma imprint" but I think it goes deeper than that, possibly tied to the actual architecture and how energy flows through a building.
Has anyone tried using a thermal camera alongside a simple compass to see if there's directional magnetic variation along the path? I've had some interesting results doing exactly that. Would love to know if others are seeing consistent routes or if some locations show more erratic movement.