No dinosaurs existed during any ice age — they went extinct 66 million years before the most recent ice age even began.
Here is the timeline: Dinosaurs ruled Earth for roughly 165 million years, from about 230 million years ago until 66 million years ago, when a massive asteroid impact wiped them out. After that extinction event, mammals evolved to fill the vacant ecological niches.
The most recent ice age (called the Quaternary Glaciation or Pleistocene Ice Age) began only about 2.6 million years ago — roughly 63 million years after the last dinosaur died. During this ice age, large mammals like woolly mammoths, saber-tooth cats, giant ground sloths, and cave bears roamed the frozen landscapes. Early humans also appeared during this period.
The confusion often arises because both 'dinosaurs' and 'ice ages' feel like ancient history. But in geological terms, they are separated by an enormous span of time. If dinosaurs had somehow survived to the ice age, a woolly mammoth would have lived alongside a T-Rex — which would have been extraordinary, but it never happened.
Pro tip: The ice age ended only about 11,700 years ago, which is why we have so many well-preserved mammoth fossils in Arctic permafrost — they froze quickly and stayed frozen. If dinosaurs had been around back then, we would absolutely have found their remains in ice.