If you're talking about old limited palette apps, I call that being a pixel artist.
Much like making sprites or icons, you work like it's a tile mosaic more so than painting like in Art Effect, TVPaint, etc.
You also have to keep in mind how the monitor blurs the colors. It's similar to distance on a mosaic, but monitors (at least CRT's) have a very specific blur that you try to take advantage of. That's one reason old games don't look nearly as good on new LCDs, the artists made the CRT flaws work for them.
I worked with the mouse to sketch things out, then spent 95% of the time extremely magnified cleaning up the pixels individually. I don't like my pencil or paint work at all, but pixels I can do given enough time.
I think I was pretty decent at it and had some pictures published in print mags way back in the day. I believe I would have had more published, but they actually thought I had scanned them. They even stated "scanned" in the description
I don't think they published my best ones because they thought it was just a straight scan with no skill involved, sort of a backhanded compliment when you think about it but it still pissed me off.
So it's doable, it's just that it's a different skill.
