I am new to wine making - mostly a beer guy. But, from what I have heard, you should wait until after fermentation to flavor and you can do it at any point after that. I would imagine adding the flavor before the end of fermentation (before stabilization) may introduce sugars you don't want or accounted for in fermenting. Could really alter the wine.
I am about to bottle my first batch ever and I am entertaining adding some type of sweet flavor. Its a cabernet sauvignon. I love a good dry red wine, but my girlfriend wants me to sweeten it a bit - debating still.