The cooling temperatures doomed the Norse-speaking Greenlanders. They were probably extinct before 1500 (the last contact with them was somewhat before then), so "the Little Ice Age" must have started well before 1500.
A date of ca. 1270-1300 sounds right--clearly caused by the Sicilian Vespers (1282), the revolt against the rule of Charles of Anjou. Charles was a white man (younger brother of St. Louis IX), so the evil white man is still to blame.
The "Little Ice Age" corresponds to the
Spörer Minimum and
Maunder Minimum of sunspot activity. But, no, solar activity has no real effect on the Earth, that's just silly.