Should I turn off the cold water while replacing a hot water faucet stem?
In all likelihood you probably don't need to turn it off, but I would still recommend that you do so, if only because you might inadvertently hit the cold side of the faucet when working in the area.

You know the saying - if it can go wrong, it will.  What's easier - cleaning up lots of water, or turning the valve off and back on?