The manual (pdf) doesn't seem to indicate any parameter responsible to change the labels' color. To be clear, I'm not referring to the numbers on the axis, but to the labels at the edges of the polygon.
I've used the first example taken from the solution given to this question.
I tried:
par(col.lab="grey")
before or after calling radarchart function, but it didn't work. The labels remained black.
The solution was to insert the following snippet just before calling the radarchart()
function:
par(col="grey")
Doing so one changes the specification for the default plotting color. See here for more.