The US Federal Highway Administration (FHWA) has a thorough set of guidelines for all of its signage. You can purchase the fonts through DGI Traffic.
The type used by the Forest Service is referred to as ASA Series C in the FS docs. The FHWA more commonly refers to the type as FHWA Series fonts but they appear to be the same. That name is applied to both the routed and printed type. You can read up on some of the specs at the Sign and Poster Guidelines for the Forest Service (PDF) page. Section 14.4 speaks to the routed signs.
You can see good vector close ups of the specs for routed signs in this PDF. The letterforms are easy to distinguish without the distortion of the router.
The FHWA type is available in Series A-F, A being the narrowest, F being the widest. The document Standard Alphabets For Traffic Control Devices (PDF) shows the types in all their glory with the spacing parameters.
Tobias Frere-Jones produced a full-featured replica under the name Interstate.