A cold star was a celestial object that existed in a dream shared by Rory Williams, Amy Pond and the Eleventh Doctor, created by psychic pollen that had become lodged in the inner workings of the TARDIS.
Unlike a normal star, the cold star "burned" cold. Whereas other stars emitted warming radiation, this apparently endothermic star caused temperatures to plummet as one approached it.
The Doctor claimed he had never encountered a cold star before this. Amy, Rory and he were sceptical such a thing could exist. After the resolution of the dream states ended the apparent threat, it remained unclear to the Doctor and his companions whether such an object could exist. (TV: Amy's Choice)