In my experiences it has been 50/50. I have been told I would have to pay an upgrade fee but most recently I have had three straight flights that they allowed me to switch to the earlier flight.
I fly to Pittsburgh often from Philadelphia and which plans leaving every 2 hours. I find sometimes I get to the airport early and the earlier flight has yet to leave so I always go to the counter to see if they will switch me.
If that person is to say no then I walk over to another counter and ask another Southwest employee - if they decline I leave it alone and go to the airport bar to catch up on the news and have a brew
Good luck!!!