We shot a whole lot of 20", even 18" barreled .308's in the service with no problem at all.
I would not go shorter than 24" with a 300wm or other magnum 30 but with the faster powders and low volume used in .308's you might even get away with 16". To ensure you never have a problem with ATF though or your state authorities I would go no shorter than 16.25".
In fact it would probably be a really, really, REALLY good idea to ensure you are not going to go below whatever barrel length minimum is allowed by not just your state but any states you might be passing through or hunting in.
I can't tell you just how badly we need uniform firearms laws nationwide... .