I didn't see a teddy bear in the trailer but I'll take your word for it.
Teddy bears, toy bunnies, dolls and all other related paraphernalia in the midst of a warzone is an old trick to tie the destruction going on around the characters to more normal life. It's a less than subtle way of saying "Innocent people died here! Be sad!" Call of Duty is all about cinematic gameplay, so I'm assuming that's why it was put in.
Another thing, you'll usually find a character goes to pick them up, and they'll almost always be blown to bits by a nearby landmine. Full Metal Jacket had a character do this, and he died. I could swear that Downfall also had something like it. I even remember seeing a baby carriage in Fallout 3, only to approach it and have a mine blow up in my face.
EDIT: Just remembered, a kid dropped a teddy bear in the very first cutscene of Red Alert.
Further Reading [http://tvtropes.org/pmwiki/pmwiki.php/Main/EmpathyDollShot]