Slow dripping pipe freeze?
Since you said "hard freeze", I'm guessing your from an area where it normally doesn't get below freezing.  If this is the case, and the cold temperatures aren't going to last more than a day or two. You likely won't have any problems, since the heat from the home should keep the water above freezing (assuming the plumbing is in conditioned space, before going outside).

If you have a shutoff for that faucet inside the house, I'd definitely close that one and open the outdoor faucet. 

If the freeze is going to last a few days, you could open the faucet a bit to allow the water to trickle.  Moving water tends to not freeze as quickly, so letting it run could prevent it from freezing.

There are also insulated hose bib covers available, which can be installed to prevent freezing. Since your bib is leaking, this may or may not work.