Longbeard is just a nickname really. Basically when people say longbeard they are talking about a mature tom (male) turkey with a "long" beard. :-) Yes you can hunt in the fall as well. However, fall turkey hunting is quite different.
Spring is the mating season and where all the excitement is in turkey hunting. You have to use your skills to compete with live hens and possibly other hunters to entice the tom to come to your location and harvest him which is the hardest part of turkey hunting basically.
In the fall the eggs that hatched after mating season are now poults and the turkeys band together in flocks with mostly hens and the poults and the toms into their own little groups since there is no competition. During this season you basically act like a turkey scattered from the flock.
I think this site might help. I found it looking around or you can get a lot of information from your the conservation department in your state.
http://www.dto.com/hunting/article.jsp?articleid=705
Also I think this sort of answers your other post as well. Hope this helps.
You can also check this link which is on this site.
http://www.huntingnet.com/articles/a...rticles_id=373