IIRC Spanish horses, which provided the main stock for Amerindian horses, are not as cold tolerant as Scandinavian horses are. This would be very good for horse breeding, since you don't have the problem of winters on the Northern Plains decimating the horse stock forcing groups like the Sioux, Cheyenne, Blackfoot, etc. to trade with (or raid) the Comanche, Kiowa, etc. for horses. This gives a greater strength to the Northern Plains. The extra few centuries gives the entire Americas more of a time to develop a sustainable model for harvesting bison, since OTL they tended to believe bison were supernaturally spawned and thus suffered famine when they overharvested bison in famine years (and worse, when the bison were targeted for game hunting as a means to destroy the locals as OTL). It's noted that the sudden abundance the Plains Indians had of bison when they gained horses compared to what they had before led them to an unsustainable harvest (noted in Euroamerican sources where they'd be dominant and powerful in some years yet be a starving and miserable people in other years), which they had to supplement with violence against other American Indians or Euroamericans, like in Spanish New Mexico or Tejas--the Pawnee IIRC voluntarily accepted US rule since they were so scared of the Sioux, and other peoples likewise expressed or were described as utterly subjugated. It helps the Lakota if they don't need to worry about planting crops much, since they can tell their vassals like the Mandan to give them those crops (in exchange for bison parts).
But horses in the Mississippian civilisation will change a lot. OTL, even groups like the Cayuse and Nez Perce were good horsemen despite being far from the Plains. I think the South and Midwest provide plenty of room for horsemanship. That could lead to local Mississippian chiefdoms expanding their influence far beyond what they otherwise could. It would be spread to the Plains, which will spread to Northern Mexico and beyond (whoever rules the Valley of Mexico, like the "Toltecs", will be invaded and conquered by these "Chichimecs"). You could have an earlier Plains Indian sort of culture, like the later Apache, Comanche, IIRC, which TTL would be mostly Caddoan in language and culture. The Mississippians would now have horses, which could innovate plows, and also provide a good food animal. Horses will be used for riding, draft usage, and food. This will strengthen the Mississippians, and make them much stronger when they meet Europeans.