How can I insulate a room without tearing down walls?
Foam insulation can be injected into the stud cavities. A contractor will drill one hole in each stud cavity to inject the foam through. Then you can patch the holes and paint over them.

You should also check any windows in the room. Look specifically at the caulking around the frame. If it's old and dry/cracked, remove the old caulk, use window/door expanding foam to fill large gaps, and apply fresh caulk.

You can also purchase window insulation kits that use double sided tape and secure a plastic sheet all the way around the window frame. Then a hair dryer/heat gun is used to shrink the plastic sheet in place. The trapped air provides a bit of insulation, and the plastic stops drafts.

If there are any exterior doors in the room, check the weatherstripping for wear and cracks. Consider replacing/upgrading the weatherstripping to stop drafts.