Dead Space 3 is gunning for release on February 5, 2013, and according to EA and developer Visceral Games, PlayStation 3 and Xbox 360 demos will be available to the public on January 22 via PSN and Xbox Live.
Xbox 360 owners actually have the opportunity to try out the demo even earlier than that. Registering your Origin ID on the Dead Space 3 demo page will net you an early-access code for the demo, redeemable on January 15. There's currently no word of a PC demo.
There's also a new trailer to catch folks up with the story so far: