sounds like the milk has gone off. I am a self-professed tea expert (LOL) and have never experienced this particular phenomena. I've made Desi Tea, English Tea, Builders Tea (

and this hasn't happened. What is your process and what materials (type of milk/teabags/teacups etc) are you using.
BTW: Tea made in Bone China, Glass & Pyrex tastes much better than other types of cups.

Just my opinion.
Also, in the Dead cold of winter, are you warming up your cups before you make tea? (not that this should make any difference to the milk splitting); Are you warming the milk?