A steppe is a vast grass land--your images show what steppes looked like. It is precisely because trees and undergrowth could not survive in the periglacial regions (very, very cold, high winds off the ice sheets) that many grasses could not just survive, but take over the flora of the steppes. Trees and shrubs and many of the flowering plants only survived in the gallery forests of deep-cut river valleys. It appears that each species specialized in one of the types of grass available. The megafauna arose because of the abundant grazing, and the necessity to carry a lot of fat and a heavy coat. As prey animals went, so went the predators--short-faced bears, cave lions, cave bears--these predators exploited the megafauna.
The grasslands you have provided images of are the kinds of environments (minus the trees) that one would have found on the periglacial steppes, but the climate, even in high summer, would have been much, much colder. The megafauna needed to store lots of fat, and to have thick hides and heavy fur coats--by spring, their fat would have been nearly all used up. Humans were attracted to these herds of game, despite the harsh climate, because one aurochs, or giant deer, or giant bison provided so much food and material for clothing and crafts, and the periglacial steppes were awash in animals. The shifts humans made to survive on those steppes are impressive, too. They had lodges half buried in the earth, with the side walls and roofs made from mammouth bones and the bones of other megafauna, over which grasses and mud were slathered. They had fire pits near the entrances, with underground vents to bring in air like a bellows. They were incredibly adroit in surviving and enviroment which was harsh and unforgiving, but which offered so much to the survivors.