Sure, why not? After all, global warming isn't warming the planet as much as it's throwing weather patterns out of whack, and some of the naysayers claim this is just what happens between ice ages—therefore we're heading towards another one and there's nothing we can do to stop it. Either way, it's entirely possible we're heading for a massive freeze*, something that's been used in Hollywood blockbusters and certainly fiction (click, click, click, click, click, click), the latest being in 2002.
We wouldn't cope very well with an ice age. Watch the movie below, then read this link, then come back here.
I doubt all the possibilities of a 21st century ice age have been dealt with. The Day After Tomorrow shows us the slightly silly, slightly scary entertainment value of the event, and the summaries for the novels I linked to** seem mostly to be stories of survival after the fact, revitalized civilization, new cultures, and people moving on.
What about a gritty, hard-SF take on an ice age as it's happening?
Problems for modern civilization as taken from the 1998 ice storm
- lack of electricity as the power lines fall, unless you have a generator
- lack of heat as the electricity goes, unless you have a wood stove
- travel made difficult, as cars will be iced in or too cold, the roads will be undriveable, few people in cities have skis or snowmobiles, and planes can't take off
- difficult travel means difficulty rescuing people and difficulties getting food
- difficult travel also means difficulties getting to work, which means economic trouble
- lack of heat means animal deaths, esp. of pets and food animals (wild animals tend to have better survival instincts and back-up plans)
- lack of communication, as computers, phones, televisions, and radios all rely on electricity
- exorbitant costs to repair infrastructure (and is it even worth it, if the ice'll just wreck it again?)
- the ice's weight nearly took out bridges, and did take out buildings (and power lines)
This will (and did) result in dead people, and it lasted only a second, geologically speaking. What if it'd gone on longer, or over a wider area? The last glacial maximum covered all of Canada and northern Europe, and some of the US. If that happened again, there would certainly be millions of refugees heading to South America and Africa, which could cause all kinds of interesting changes to those continents. New England would be leveled, so there go New York and Washington D.C., causing massive political and economic upheaval. (And you thought the recession was bad!) And places that are tropical and/or balmy now would be cooler. There would definitely be extinctions.
In the long run, we'd probably deal with the ice by inventing new vehicles and buying skis, by living a simpler life without electronics, by not overeating, and by shifting our centers of power to more southern latitudes. Our ancestors would've hunted for food, but we'd endangered a lot of game animals through overhunting and ecological mismanagement, so we'd have to keep relying on cows, sheep, pigs, and chickens, but that would mean finding a way to keep them alive to grow and breed. We'd also need to solve the warm clothing problem—How will we manufacture it if we don't have electricity? How will we transport it? Will we go back to fur?
In the short term, though, we'd be scared, desperate, cut off from anyone outside our city or town, and probably resort to a band mentality, with the requisite hunters and group defenders, and one or two people taking control. How would that play out with the current social classes and current professions? Yes, it's cliché to have the lawyer try to seize control because he's used to it, and failing as the lower-class man proves himself, but I still kind of see that happening. There'd probably be murders for control as well, as everything progressed and bands met up with each other.
Of course, I can't imagine everything, but hopefully I've inspired someone enough to a) further discussion or b) see a book like this on the shelves in four or five years.***
*and entirely possible we're not
**what, do people expect me to read everything?!
***that's about how long it takes.