The zoo Reindeer were killed by insect-borne viral hemmorrhagic fever. I'd assume the local White-tailed Deer population served as the viral reservoir, but the disease itself is more prevalent farther south in the United States and only recently appeared in Minnesota so there is probably a weather/climate link there.
As for the loss of native Woodland Caribou from the Great Lakes region (including Minnesota), there are a combination of factors. Most of the area is still forested, but rather than lichen-rich spruce/fir forest, there is now more aspen and maple that have grown in since logging took place. This allowed more White-tailed Deer to move into the region, which compete with Caribou, serve as carriers for diseases (including hemmorhagic fever but more notably brainworm), and support larger populations of wolves. Caribou were also extensively hunted in the late 19th and early 20th century. The result is the retraction of the range of Caribou to the north, with the last mainland population of Great Lakes Woodland Caribou (in Pukaskwa National Park, Ontario) currently in the process of going extinct and the last island populations in Lake Superior requiring intensive management, including predator control.