I've used latex and acrylic paints both in outdoor use on paper mache, and they hold up quite well without further weather proofing (well, at least in the light rains we have here - nothing compared to the heavy stuff some people receive).
The one thing to watch out for, and this will be true for any material you use to weatherproof mache, be certain your coverage is sufficiently complete.
I found this to be the case on a witch head I had put together - the paint on the face held together as the head collapsed in on itself - it turned out I had failed to put enough paint on the back of the head (had given a light coating, and as it wasn't going to be showing, I didn't think anything further of it - much to my later miserable amusement).
The one thing to watch out for, and this will be true for any material you use to weatherproof mache, be certain your coverage is sufficiently complete.
I found this to be the case on a witch head I had put together - the paint on the face held together as the head collapsed in on itself - it turned out I had failed to put enough paint on the back of the head (had given a light coating, and as it wasn't going to be showing, I didn't think anything further of it - much to my later miserable amusement).