My theory is the humans of the time, cave dwellers as well as plains, being mostly herbivores created so much methane gas that it disrupted plant life cycles to the point of extinction and when the cold snap happened, the humans shifted to animal flesh to sustain themselves and ate everything up. Then they all froze.
That's my theory.
But extinctions of the megafauna didn't all occur at the same time around the globe. South america lagged almost 400 years behind north america in mammoth extinction.
Siberia also lagged behind. Also, on islands some persisted for a long time. That kind of tips it to humans as a factor.