In quite a few depictions of the Buddha in artwork, he appears androgynous.
Does this represent something significant in terms of a Buddhist message or ideal, or is this just an artistic style?
It's an artistic style. The impression of androgyny is arising in the mind of the viewer (not necessarily every viewer), and part of its cause is our arbitrary cultural standard of how men and women should look.
A young lady named Kisa Gotami, seeing prince Siddhartha in the street, uttered:
“Nibbuta nuna sa mata - Nibbuta nuna so pita Nib buta nuna sa nari - Yassa’ yam idiso pati.”
“Peaceful is the mother who has such a son. Peacefull is the father who has such a son. Peaceful is the wife who has such a husband.”
So you can imagine how the artwork should look like.
India's first prime minister Shri Jawaharlal Nehru once wrote in his writings, that, while he was in prison, he hung a photograph of the Buddha, and he stated that this particular Samadhi Buddha statue(in Anuradhapura) photograph brought him much happiness and solace when he was in the cell.
You can also study the 32 major and 80 minor physical characteristics of the buddha to get an idea.