First Ice Age
The First Ice Age occurred in the time of Neanderthals. (TV: Ghost Light; AUDIO: The Exxilons) During this time, an Ice Warrior craft from Mars crashed and buried itself. (TV: The Ice Warriors) One Neanderthal was preserved by Light. (TV: Ghost Light) The Dæmons visited Earth, and according to the Third Doctor, inspired cave paintings of powerful supernatural beings. They favoured humans over Neanderthals, causing the latter to die out. (TV: The Dæmons)
How can whole glaciers just pop up out of nowhere? Well, they just did. That's how this planet grows - a series of catastrophes. Farewell to the Ice Age. Welcome to the Tree Age. Possibly. When the Ice Age was here, you lot managed to cook mammoth. Now there's a forest, you'll just have to eat nuts.
Second Ice Age
Earth suffered a Second Ice Age circa the year 5000, a time period visited by the Doctor during one of his four incarnations (TV: The Talons of Weng-Chiang) and, later in his life, during his fifth (AUDIO: The Butcher of Brisbane) and eighth incarnations. (PROSE: Emotional Chemistry) The Second Doctor met the thawed Ice Warriors during this time. (TV: The Ice Warriors)
Behind the scenes
Publicity material for The Ice Warriors sets that story in the year 3000, but no other stories occurring around that era mention an Ice Age. In the televised story, it is described as the "second Ice Age" whereas in the novelisation it is called the "New Ice Age". The Fourth Doctor mentions an Ice Age in 5000 in Talons, but in that story's novelisation there is no mention of an Ice Age. In the comic story The Keep, Earth is ravaged by solar flares in the 51st century instead of an Ice Age.
It is worth noting that during the Ice Age, only part of the planet was covered, not the entire world, so there is some room for discrepancies.