Scientists can tell there was ice because we find rocks from those times that have marks from being scraped or moved by glaciers - huge frozen rivers of ice flowing slowly down mountainsides. Some of these rocks were found in areas that, at the time, were in mid latitudes or even the tropics - imagine ice and blizzards in the Caribbean!
There are many things that can push Earth towards an ice age, and when several of them occur together, it can shift the environment far enough to cause glaciation (the process of covering Earth with ice) to begin. The sun has become hotter over time, greenhouse gases increase and decrease, the orbit and tilt of Earth fluctuates, and the movements from plate tectonics and geological activity continue to change the planet we live in. All these environmental factors play a role in creating an ice age like the one our Mastodon, 'Max', lived in.
All these factors react with each other and themselves in a complex dance that determines the climate of Earth. For example, ice is white and reflects sunlight very efficiently. When ice begins to spread, more sunlight gets reflected away, which makes the Earth cooler, which causes the ice to spread even more. Once you get a feedback loop such as that going, it takes a lot to get it to completely stop, and that is how ice ages can begin.
About 12,000 years ago, the last glacial period ended and we entered a warmer interglacial period. Technically, we're still in an "ice age" - if there's ice covering large portions of the Earth, like it does in Antarctica or the North Pole, it's still considered an ice age - though right now we're in a relatively warm period where most of the ice has gone. That could change, though, if we enter a new glacial cycle. The geological record shows that's probably going to happen between 28,000 to 88,000 years from now....so probably no need to go buy a heavy jacket and a snowmobile just yet.
DJ and DA