Can't do it now but have hopes of building a self bow or two in the near future.

We had a big storm a little over a week ago that got me thinking about this.  The storm was basically 60-80 mph straight line winds that knocked down a lot of trees and large limbs across the region. Over the next few days a LOT of wood began to show up by curbs for the city to pick up. Because of the severity of the storm they decided to send crews to pick up the wood and offered a place for folks to take and drop the stuff for free. They said it could take a couple months to cover all the area affected by the storm. I was thinking that it might be a good place to go and see what you could find at the site. OR just drive around and look for down trees/large limbs to take off people's hands.  
How long can a tree be down and still be OK to use?  Would it be OK to go to the collection spot and pick up useable pieces of downed wood after the fact and again.....how long is too long?  
Just thought it might be an opportunity to put some good pieces up to dry.

Thanks!!

Osage, black locust, & mulberry should be fine for a while.  White woods like hickory, elm, & hackberry go bad quickly if they are not split and elevated off the ground in a dry location soon after they are cut

What Dan said. The sooner you can collect the wood and properly store it the better. I wouldn't use wood that was in the elements for more than a couple of weeks and even that can be too long or some woods. Rot resistant woods like osage, locust, mulberry, like Dan said sould be OK if left on the ground but the sooner you deal with them the better.