Above are two samples of the script font used by the National Park Service.

The closest match I have found are the two Sign Painter fonts below:

Unfortunately, A) they do not come with a bold style so I used faux bold in Photoshop which isn't ideal and B) they are still not close enough.

If you can suggest a font that resembles the National Forest font more closely, please email me at randy@joeinfo.com

Thank you very much!

I've gotten quite a few inquiries and it sounds like the forest service uses a handwritten version.
As far as fonts go, the most frequently mentioned is Brody. Here it is: