Found this tutorial for creating a transparency mask (it's for V3 but tried it with H3) so the eyebrows can be changed into different colors.

http://www.daz3d.com/i/tutorial/tutorial?id=2159&_m=d

Followed it step by step, the settings look the same, but the eyebrows don't appear in the preview or render.  One issue is that H3 does not have an eyebrow body part, nor does V4 (in PPro 2010).  But it does seem to be visible because if transparency map is removed or the trans dial set to 0, the eyebrows are a solid color.

Can anyone help with the tutorial?  Will it work with H3?  Or is there a better way to change eyebrow color for H3?

I can assure you that V4.2 does have an eyebrow part. Are you using V4.2? If not, you need to upgrade. V4 had serious issues. Just keeping her around for Obj2Cr2, which needs her - it spits the dummy when you give it V4.2.

Yes, I use V4.2.  I'll check again.

But, should this work with H3?

Just loaded a V4.2 and see the eyebrow body part.  That other figure was Aiko 3, not a V4.2.

Tried it with V4.2, it works.  H3 doesn't have an eyebrow body part to make visible, or it's hidden.  There is an eyebrow material.

Any other ways to make a good different colored eyebrow for H3 on a given texture?

It's odd.  If the eybrows are set to a color with transparency off (0) then the brow is that solid color.  If the transparency is 1, the colored brow disappears to show the face texture behind it.  Even if a trans map is applied, with transparency 1, the H3 eyebrow isn't seen.

Do you have a MAT Room screencap of your node arrangement and a view of your transmap?

Images sized down for post, view image to see at full size.

Here is the transmap.

This is the transmap that came with the material:

This is the material room for the skin head material.  This is the edited material with eyebrows removed:

This is the material room for the eyebrow with transparency set and transmap applied:

This is material room for eyebrow with the transparency at 0.  Not that the eyebrow is then a solid color.

I can use an eyebrow brush to paint on new eyebrows (directly to the head material), but that painted on eyebrow doesn't move well when the figures eyebrow is moved, and it means painting a new texture for any eyebrow color change rather than just changing a color in Poser.

Full size imaging is not working.

Edit:  I just looked at the tute, did you try changing the diffuse_color to something other than white?

Yes, that is supposed to change the eyebrow color.  But the eyebrow still doesn't appear unless transparency is 0 or close to 0, then the eyebrow on H3 is a solid color. 

Here are the full size images.

Transmap that came with the set.  It works for the eyelashes.  Change diffese eyelash color and the eyelashes change color.

This is the map created following the tutorial.

This is the material for the skinHead with the eyebrow-less material applied:

This is the eyebrow material with the new transmap applied and transparency settings (1).  Note the eyebrows do not appear.

This is the material with the new transmap applied with transparency at 0.  The eyebrows are there, a solid color.

Not sure if you said, but for the Eyebrows zone, in the Parameter dial window, do you have it turned on to visible (second tab, first tickbox)?

There is no eyebrow body part in the list for H3.  There is an eyebrow material, but no eyebrow body part.

There is a dial "BrowsGone" on the head.  It is set to 0 so the brows show, which is proven when the eyebrow material transparency is 0, they are visible as solid colored eyebrows.

Terrific, it works.  Thanks.

In PoserPro 2010 it doesn't show in preview (eyebrows are not visible) but does in the render, but that's fine.

Yeah, this always threw me whenever I needed a transmapped eyebrow. I could never remember the specific combination of dials to get them to work until I wrote it down on one of those blank pages in the back of the Poser manual.

I was about to respond but I see you've got it.  ; )