Should shut off valves be installed on outdoor faucets? Mine currently does not have one. It's an older house.
If you live in an area with freex\zing weasther, yes.
The hose bibs need to be cut off snide the heated space, then opened to drain.
You can sometimes get away with 'frost proof' hose bibs.
they are long enough the valve is inside heated space.
Install one not pitched correctly (or leave a hose attached full of water) and it will not drain and freeze anyway.
It is a frost proof type with the valve in a heated space. Not sure how well it drains but I disconnect the hose in winter when it freezes.
If it is a house that has made it through a bunch of winters already with this setup, then you probably are fine. If you are in doubt, they sell covers for the outside.
I think the frost proof long valves where the seat of the valve is inside where it is warm, are the best type. The secret of course is to not forget to disconnect the hose. If you leave the hose on, it will not drain, and freeze up. Guess why I know?
If you go with the inside shutoff valve system, then you also need a drain valve inside. They most often end up in really awkward positions and are a pain in the butt to use. And, again you have to remember to drain them each year or guess what? Been there too...