Plants during the age of the dinosaurs were no larger than the largest modern ones. During the Mesozoic there was a shift in dominance between gymnosperms (conifers and others) and angiosperms (flowering plants), but this happened in the Cretaceous, in the middle of the dinosaurs’ dominance.
It’s an open question of why dinosaurs got so much larger in the Mesozoic than mammals did during the Tertiary. Changing levels of carbon dioxide (which could have increased plant productivity) or oxygen (which could have permitted greater activity) could have had something to do with it, but these changed throughout the Mesozoic and this can’t be a general explanation.
Sauropods may have been able to get so big because of their highly efficient feeding apparatusand their physiology. Mammals by happenstance have not been able to duplicate this system. The largest carnivores may have evolved to exploit the large sauropods. Dinosaurs in other groups were generally within the range of size reached by the largest mammals, such as Paraceratherium (Indricotherium).
The asteroid strike that killed the dinosaurs did not change Earth’s axis. The most recent ice ages did not start until about 2 million years ago, most likely due to changes in oceanic currents triggered by the closure of the isthmus of Panama. There were no ice caps on Earth at any time during the time dinosaurs were dominant, although there had been ice ages before dinosaurs evolved.