Reddit reviews Changes in the Land: Indians, Colonists and the Ecology of New England

Native American deforestation differs significantly from European settler deforestation, especially in the Northeastern US. Specifically, Native Americans seasonally burned underbrush, leaving the larger trees intact, to make it easier to hunt. When they cleared land for farming, it was in small parcels and only cleared for a couple of seasons, after which the plot was abandoned and regrew quite quickly.

The 'California-sized' area of deforested land is, IMO, a gross overestimate that probably does not account for the temporally fragmented nature of Native American land use patterns see Changes in the Land by William Cronan for more details. Furthermore, colonial-era deforestation followed quickly on the heels of Native American population decline and was of the clear-cut variety- completely denuding the landscape to make way for pasture, heat homes, harvest timber, and fuel paper mills.

That said, I have a hard time believing that Native American deforestation had any significant impact on global climate on the scale of the Little Ice Age.

It's an interesting idea but back-of-the-envelope calculations don't fully support their hypothesis.

William Cronon's Changes in the Land is another fantastic look at this. He focuses on New England but he goes in great detail about the various Indian cultures that were there before Europeans arrived and what happened to them as a result of disease, as well as how this affected the ecology and climate of the land.