When the sign is on the main road it usually just means that the road is closed.  With our wet winter and spring a lot of the roads in areas need to be repaired and when they are single lane roads it doesn't give them much room to work.  The National Forest is also in the process of closing off side roads and logging roads that people have used for years and years.  If it isn't on their official map then it is going to be closed.  They will do this by either blocking it with boulders or large pile of dirt to where you shouldn't be able to go over or around it.  As for hiking I don't believe that they would bother you if you headed out on the side of the hill away from the road where they are working at.  Or where it looks like they are working

I have never run into this problem myself other than a few seasonal closures on some BLM lands. Like Critter said the only thing I have run into has been road closures for the winter that are always opened up again when the roads are good enough to use without causing more damage. But these roads always have gates so you know very well if they are open or not. Basalt mountain has these in 444 as well as the crown in 43. I have never run into a situation where you were not allowed to continue on by foot though.

That is good to know.  The only reason I even doubted the on foot access was because some of  the signs said things like "Wilderness Trailheads Closed" and "Authorized Personell Only".  This was in Unit 29 west of Boulder, so I thought they might be a little more sensitive to these closures since it is such a high use area.  

Our main reasons out here for national forest closures are fire danger.  They seem to think that the use of vehicles could start a fire, or someone shooting at something, causing a spark, could also start a fire.

It's very rare though.  More likely, as Critter said, it's usually just a road closure of some kind.  The local offices should have an answer if you call.

BLM is notorious for closing their land out here to motorized access.  The dirtbikers and ATV'ers don't seem to respect the "no off road vehicles" signs, so they close the entire road system down to let the unauthorized trails grow back over.  Some people don't get the hint.

So, I finally called the Boulder Ranger Station, and inquired about these closures.  I found out that the vehicle trails that were closed for construction/reconstruction are closed to vehicle traffic completely for the rest of the year.  Any of the construction areas are closed to foot traffic where construction is taking place.  Some of the trailheads in the area are closed to foot traffic.  However, off trail hiking is still allowed, just not encouraged.  

This does make my scouting a little more difficult, but I think it is great news for my hunting season.  This should keep quite a few people out of those areas.  

Most of New Mexico is in stage 3 fire restricions.  which means closed to all. Only a few areas are back in to stage 2.  Its going to be a long summer/fall if we don't start getting rain.