Snowman, Icicle, Ball, Bell, Santa Hat, Top Hat, nutcracker, and stylized elves, and peppermint rings are all great examples of ornaments that can be made on a lathe.
In this video I am making an icicle snowman. This is a fun spindle project which gives you great practice rolling beads and using the skew chisel. It is quick to make and can be batched out fairly easily. They can be decorated with paint with a couple dots for buttons and the face. Or the entire thing can be painted with small children.
The Icicle Snowman was popularized by production turner Nick Cook. He did one at a demonstration in April and it looked like a lot of fun. I added a middle section to the snowmen for more of a traditional look.