The only café facilities (in the arrivals halls) open overnight are those provided by Costa in Terminals 1 and 5. (Remember that you don't need to wait in the terminal that your daughter's flight will arrive at; you can wait at another terminal. Terminals 1, 2 and 3 are all within a 10 minute walk of each other. Terminals 4 and 5 are linked by free buses and trains).
There's theoretically no reason why you can't wait overnight. As others have indicated, it won't necessarily be a particularly comfortable wait (which is why I've told you where to find Costa) but, as long as you don't look like either a vagrant sheltering from the cold or a terrorist looking for a target, the security staff shouldn't trouble you. (They're used to people waiting for the arrivals of severely delayed flights, so there are often people there for several hours).