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I can't see any possible causation between the Black Death and the Little Ice Age.

Scientists have tentatively identified seven possible causes of the Little Ice Age: orbital cycles; decreased solar activity; increased volcanic activity; altered ocean current flows; fluctuations in the human population in different parts of the world causing reforestation, or deforestation; and the inherent variability of global climate.

The Black Death is estimated to have killed 30% to 60% of Europe's population. In total, the plague may have reduced the world population from an estimated 475 million to 350–375 million in the 14th century. It took 200 years for the world population to recover to its previous level. William Ruddiman proposed that these large population reductions in Europe, East Asia, and the Middle East caused a decrease in agricultural activity. Ruddiman suggests reforestation took place, allowing more carbon dioxide uptake from the atmosphere, which may have been a factor in the cooling noted during the Little Ice Age. Ruddiman further hypothesized that a reduced population in the Americas after European contact in the 16th century could have had a similar effect. Other researchers supported depopulation in the Americas as a factor, asserting that humans had cleared considerable amounts of forest to support agriculture in the Americas before the arrival of Europeans brought on a population collapse. Richard Nevle, Robert Dull and colleagues further suggested that not only anthropogenic forest clearance played a role in reducing the amount of carbon sequestered in Neotropical forests, but that human-set fires played a central role in reducing biomass in Amazonian and Central American forests before the arrival of Europeans and the concomitant spread of diseases during the Columbian exchange. Dull and Nevle calculated that reforestation in the tropical biomes of the Americas alone from 1500 to 1650 accounted for net carbon sequestration of 2-5 Pg. Brierley conjectured that European arrival in the Americas caused mass deaths from epidemic disease, which caused much abandonment of farmland, which caused much return of forest, which sequestered greater levels of carbon dioxide. A study of sediment cores and soil samples further suggests that carbon dioxide uptake via reforestation in the Americas could have contributed to the Little Ice Age. The depopulation is linked to a drop in carbon dioxide levels observed at Law Dome, Antarctica. A 2011 study by the Carnegie Institution’s Department of Global Ecology asserts that the Mongol invasions and conquests, which lasted almost two centuries, contributed to global cooling by depopulating vast regions and allowing for the return of carbon absorbing forest over cultivated land.