Exterior faucet - freeze hazard?
The key question would be: How many winters has this pipe been like this and lasted without bursting? If it has made it through for many years, it should probably be good for many more.

Does it have an indoor valve where you can turn it off and drain the water, similar to this:

http://www.homedepot.com/p/Everbilt-3-4-in-Brass-Sweat-x-Sweat-Ball-and-Waste-Valve-with-Drain-119-4-34-EB/205812172

If so, then you can just shut off the valve and drain the water.

The safest/best/permanent solution would be to install a shut-off valve like above (make sure the drain hole is on the "to the outside" side of the valve) and also replace it (or have it replaced) with an anti-siphon frost-free outdoor valve like this:

http://www.homedepot.com/p/1-2-in-x-12-in-Brass-Anti-Siphon-Frost-Free-Sillcock-Valve-with-Push-Fit-Connections-P140-8-12x12/203518399

For a "quick fix", you could wrap it with a short length of heat tape:

https://www.amazon.com/dp/B002YFAHAW/ref=twister_B0048BPXDG?_encoding=UTF8&amp;psc=1 

and then some pipe insulation: 

http://www.homedepot.com/p/Everbilt-3-4-in-x-6-ft-Foam-Pipe-Insulation-ORP07812/204760801