I've always wondered what exactly happened with the Day After Tomorrow's ending. So pretty much most of the planet has been encased in ice. Majority of Western governments are either non-existent or have fled to previously designated Third World Countries...but what then? Millions have been left behind and such a rescue effort would be enormous and a wide-scale task such as this would be both risky and time-costly. No doubt most of the effort would be to concentrate on keeping the people safe in the countries which have so graciously welcomed their First World lodgers.
The RP would be story and character focused in nature. Thus no real sexual content would be a significant part of the story. Not saying it's not allowed; just keep it realistic. No wanton sluts or man-whores. Also despite these kind of plots to be American-centric (for no reason at all) it would be best for us to be part of the American refugees. Of course for national diversity you could say your character is an immigrant. That's what I'm going for. Our characters would be part of a team that venture into the frozen North. These teams are hired or commissioned to map out the new landscape, search for supplies and survivors. Equipment would be self-found. Things like cold-weather gear would probably be issued but any weapons would have to be stolen, scrounged or taken with the character during the initial evacuation.
In regards to the year...well the movie was released in 2004 which I'd assume to be the setting for the movie. 2016 seems viable enough for the US government to get its act together and start forming some ruling on their population. It would also give rise to probably some Fallout and Mad Max-styled raiders (though not as insane) adding another, but not original, line of threat on top of the dangers from the new climate and landscape.