One day an ice age will return. Assuming it happens with a society more like ours than one that could leave the planet or employ other outlandish strategies, how would we respond? What percentage would migrate? How would we feed ourselves? I imagine far more people would die from hunger than from exposure.
The biggest question, as I see it, is how quickly an ice age comes on?
As you state, "human civilization" is basically ~10,000 years old. But human technology has basically expanded exponentially during that time. We can restrict "civilization" to largely starting with the Sumerians, 6000 years ago. The Chinese can draw back ~5000 years. We get closer with "western" civilization perhaps starting with the Greeks, 3000 years ago. Continue through the Romans, and then the dark ages, and I'd say we don't get all that close to anything even approaching "modern" until at least the Enlightenment. That was the rise of the study of natural history and modern science. So we're down to 400 years or so.
The true technological age that we recognize is maybe 400 years. Only the last 100 or so would be what we even consider truly "modern" when it comes to mobility [automobile/locomotive/air travel] and communication [telegraph/telephone/radio/TV/internet].
If we were to "plunge" into an ice age, on the scale of within 25 years, I think humanity would be well and truly f$&#@d. Over a time span that short, the displacement of people would cause incredible demographic and geopolitical strife, and I think it would cause war and desolation.
However, let's say that an ice age takes 200 years to really form? In that case, I don't think it's anything we're worried about. We'll either have more than sufficient technology to adapt to the changing climate over that time, or we'll have killed ourselves off through more conventional means (nukes, Skynet/Matrix-style AI, bioterrorism, gray goo, etc) and won't be here to worry about it.
A quick googles search of "how long does it take an ice age to form" was inconclusive, but I suspect it's a more gradual process than the premise of your question supposes.