I wouldn't use the term deforestation. They absolutely utilized prescribed burning. In the eastern USA, this had the effect of clearing the understory. They did this primarily to improve hunting.

In the west, this kept the prairies as lush grasslands. In the southern plains, these fires keep eastern red cedar in check, and it created nutrient rich young growth of short grass and tall grass species that game (bison and elk) frequented to graze. In the northern prairie, it kept rivers free of trees. The Platte River was renowned for being wide, shallow, and mostly without trees. When those fires stopped, trees encroached up the river, and eastern bird species used these as highways to colonize western states in which they did not historically occur.

Trees, prairies, and prescribed burning had a long history in North America before the arrival of Europeans, thousands of years. The interruption of these burns has thrown many species into disarray.

Habitat specialists that evolved along with Native American burning are affected the worst: Kirtland's Warbler Black-capped Warbler

Native Americans created a mosaic of different successional stages across the landscape, but it was rotational and not outright deforestation.

Sources: Biologist, the book 1491, rangeland and forestry textbooks, basically my undergrad and graduate course work.

Edit: Conservation efforts are often focused on replicating these prescribed fire regimes.

Edit2: Black-capped VIREO, not warbler. Got distracted by toddler as I typed.