Reddit mentions of Evolution of Tertiary Mammals of North America: Volume 1, Terrestrial Carnivores, Ungulates, and Ungulate like Mammals

One of the best books I used was Evolution of Tertiary Mammals of North America, Volume 1 because the first chapter is an overview of the climatic changes in the Cenozoic and the second chapter is an overview of the vegetation changes in the Cenozoic. However, it is out of print, so you'll have to check a library (worldcat can help you find the closest copy available).

Evolution of Grasses and Grassland Ecosystems is probably the best overview of what you were asking about, and while it goes into detail, I don't think it's too bogged down with jargon. Mammalian Response to Cenozoic Climate Change and Using phytolith assemblages to reconstruct the origin and
spread of grass-dominated habitats in the great plains of North America during the
late Eocene to early Miocene are two more papers I recommend. If you can't access them through the links, try searching the titles on google scholar to see if you can get them that way.