Colour from the studs themselves is not really "bleeding" through the drywall, but it is the studs that are causing the problem.
When metal studs are used in outside walls of a house, they conduct so much energy through the metal that the overall R-value of an R-19 wall drops to only R-10. When the cold comes in through the stud, it cools the drywall right in front of the stud. The cooler area of the drywall collects moisture from the air, and even if the surface doesn't appear wet, it will collect dust. That dust is what you see that appears to be the studs bleeding through the drywall. Even wooden studs and ceiling rafters often do the same thing when there isn't adequate insulation, and we often see the rafters "ghosting" through on cathedral ceilings. Although wood is not always a problem, metal studs almost always are. In a cold climate it just doesn't work to use metal studs on outside walls without some kind of insulation over the stud. The insulation can be placed over either the outside or the inside of the stud, but the metal must be insulated, usually with rigid foam insulation.
Click here for an animation explaining thermal bridging and wall ghosting.