Let's start with how necromancy works in this setting. A magic-user grabs a corpse, shoves magical energy inside, and gets to boss it around until the magic runs out.
The efficiency that a corpse varies depending on its condition or how the magic-user has prepared it before animating it. Unless given very specific direction to do otherwise, magic follows the path of least resistance to reach the task the magic-user has given it. The resistance in this case is against the laws of reality (our physics). As the locals like to say, "Magic is lazy, and clever about it."
The fallout of this rule when applied to necromancy is that a corpse in perfect working condition is not the ideal target for necromancy. When commanded to make the corpse move, magic will do just that, wasting most of its energy kickstarting biological subsystems that the necromancer almost certainly doesn't care about and are not necessary for the newborn zombie to pick up heavy thing or chase away annoying adventurer. A damaged corpse is even worse, with magic trying to animate the whole meat-bag only to find out there's a hole and then waste even more magic keeping the corpse from falling apart through said hole. We will ignore that case for now.
The magical energy needed to animate a zombie is equal to the energy usage of a living human body minus the energy used by the brain, as this specific necromancy does not interact with the physical mind.
Zombies are highly inefficient, so the preferred target of necromancy is a clean skeleton. Magic is smart enough to skip trying to hotwire any nonexistent biological systems, so when commanded to animate a skeleton it instead focuses its energy on simply keeping the parts all in the right places and moving in a way that looks like how a human moves.
The magical energy needed to animate a skeleton is only the energy needed to hold the individual bones in place (there are no muscles or ligaments) against gravity, and the energy needed to physically move itself and whatever it needs to carry.
The third type of undead, a ghost, is simply the inverse of a zombie. Only the mind is reanimated, usually used by necromancers to ask the dead questions or just hang out in graveyards without feeling lonely.
The magical energy needed to animate a ghost is equal to the energy usage of a living human brain, plus a small overhead of creating sound vibrations in the air if the necromancer feels the need to verbally converse with the dead, but we can ignore that.
Now to get into the apocalyptic scenario proposed by the title of this question. One particular necromancer thought himself very clever when he came up with a spell that outsourced the cost of animating a corpse. Instead of requiring a payment of magical energy from the magic-user to get the corpse moving and doing useful work, it would absorb energy from its surroundings.
Problem 1: This completely removes the dependency the animated corpse has on the magic-user once the initial spell is cast. If corpse isn't going to run out of energy any time soon, there was never a hard rule in necromancy that the corpse had to stop moving as soon as it finished its initial job.
Problem 2: This setting has nothing along the lines of "ambient magical power." Magical power is simply another form of energy, and Magic, again being lazy, when instructed to just suck up any nearby energy to make a corpse move around, decided that the most readily available energy to use was thermal energy. So these new undead are able to continue to exist simply by lowering the temperature of their immediate surroundings. The Earthly belief in ghosts causing cold spots has officially become a reality for this particular world.
So the situation this world now finds itself in is a growing population of zombies, skeletons, and ghosts that are continuously sucking up heat to move around and continue to un-live. Assuming that all of these undead are simply walking at a casual human walking speed and not exerting themselves, my question is:
If this undead horde consisted of entirely zombies or skeletons or ghosts, how many would there have to be to plunge the world into a global ice age?
Some things I've been mulling over that might complicate what I initially imagined could be solved by a simple (or not so simple) math equation is if factors such as location or distribution affect the end result, such as if having such a large undead heat sink near the equator would alter wind patterns in a different way than if the horde was place near the already-chilly North or South poles.
