In the only jurisdiction where I've actually read the trespass law, it stated that a "legal fence" was sufficient to indicate no trespass, and that a "legal fence" was any number of acceptable structures that were at least 4 feet high.

In that context, a wall of a house being at least four feet high, would carry an implicit "No Trespassing" sign on it, but the picket fence would not. However, if the property had an obvious path to an entryway, then walking up that path to the entryway was not trespass. So walking through a picket fence with a low-latch would not be trespass, unless the pickets were four feet high, or if the latch was locked.