Small note, but we don't know if the map we see in Chrono Trigger is the entire world or not. We assume it is, but just as there are probably more people than we ever see in any given time period (else inbreeding would be a problem), there could be a lot more land that we don't see.
As for a planet-wide Ice age lasting 64,988,000 years... maybe it did, maybe it didn't. Climate cycles in the real world don't last that long, so it could very well have had numerous other ice ages during that time period. However, even if not, an ice age doesn't prevent any life, but it does limit it. During "summer" months, some regions might thaw enough to produce plant life, allowing some animals to survive. The Zealeans were familiar with the oceans, so fish could provide significant food resources, etc.
It isn't that people couldn't survive an ice age, it is just a tough existence.