First off I think it's a great song, nothing like their past work but refreshing as a result. Although I think I've overplayed it (about 15 times).
There are a few key themes in the song, first is the long and dark december with the WHITE snow, second is the Violet Hill, third is the references to war. In other words I think Chris is singing the song from the viewpoint of a soldier about to be sent off to war for reasons he cannot control and thus has no other choice.
"Was a long and dark December
From the rooftops I remember
There was snow
White snow"
He's setting the mood of the song here, a very cold desperate mood that is highlighted by the piano only being played during these lines.
Then the song gets going, as if to explain something has happened, i.e. an event has started.
"Clearly I remember
From the windows they were watching
While we froze down below"
Here I think "they" refers to those who initiated/planned/perpetrated the war, and they are now sitting up there in their warm safe homes watching below those they sent into the cold (war) freeze (suffer).
"When the future's architectured
By a carnival of idiots on show
You'd better lie low"
here the carnival of idiots refers to the perpetrators of the war (imo george bush et al), people who aren't very bright but have planned out the future of so many (the soldiers going to war and the victims of the war as well as overall implications). He is saying that when this happens it is best to lie low and out of sight or risk being sucked into their plans.
"If you love me
Won't you let me know?"
he's telling his lover that now is the time to tell him if she loves him, for she may never see him again as he is being shipped off to war.
"Was a long and dark December
When the banks became cathedrals
And the fog
Became God
Priests clutched onto bibles
Hollowed out to fit their rifles
And the cross was held aloft"
This indicates that now some time has passed from the start of war, and it is getting nowhere and with a huge cost in lives and money. Desperate soldiers look to god in hopes he will save them (their rifles a place to store the bibles) and banks (due to the high financial cost) are now worshipped like cathedrals by those who started the war (again, imo bush et al) in hopes of getting help with paying for the war.
"Bury me in honor
When I’m dead and hit the ground
My Love is opposed when unfold
If you love me
Won't you let me know?"
The soldier is now sure he will die soon in this war, and again tells his lover that if she loves him she'd better tell him soon. It also seems like he's come to the realization that being buried in honor is pointless because he will be dead, and is in other words, not all it's cracked up to be.
"I don't want to be a soldier
With the captain of some sinking ship
With snow, far below"
It seems now the soldier is having second thoughts, and decides to desert the army and run. He doesn't want to be a soldier anymore especially with the idiotic perpetrators (bush et al?) as the leaders, and sees how pointless the whole war is and that no one will win and everyone will lose. He does what any sane person does with those odds.
"I took my love down to Violet Hill
There we sat in snow
All that time she was silent still
So if you love me
Won't you let me know?
If you love me,
Won't you let me know?"
Here "violet hill" refers to a snowy hill turned violet from the blood of those who died in the war, and after running away he's returned and taken his love there to show her why he had to desert the army and what he faced and suffered. But now the army is after him for deserting, and thus again he will be apart from his lover. So again desperately he asks his lover that if she loves him she better let him know for she may never see him again. Also here the piano is the only instrument playing, to highlight the sadness and the coldness of the situation.
In short, the song is about the pointlessness and desperation that war brings, and how there is no winner either way. It highlights how soldiers are often doomed wether they fight in the war or choose to run and how sad and desperate the situation becomes. It's also fairly political with references to governments (george bush et al?) and how they initiate such sadness and desperation with no regard to anyone but themselves and no consideration of the consequences. Anyways that's my interpretation, I think there could be many for the army deserting part, and thus feel free to voice your own interpretation here :).