flash (macromedia):

Is it a dynamic textfield, or a static textfield? In the case of a dynamic
textfield you can use a CSS stylesheet. See the help files for how to attach a
stylesheet to your textfield.

In the case of a static textfield, I'm not sure if you can attach CSS, but the
help files can answer that for you. Using CSS is the way. Your stylesheet would
need to define :hover events:
a:link{
color:#ff0000;
}
a:hover{
color:#0000ff;
}