I don't personally subscribe to "children should be allowed to run around naked all the time" concept, though I know parents who do. Though I have had issues with getting my son out of his pajamas and into regular clothing.
I started by making it a rule that the first thing we do when we get up in the morning is get dressed. I do it, my husband does it, I get my daughter dressed, and my son gets dressed. At that point, getting undressed is more of a pain in the butt than just staying dressed. There is no wandering around the house in our pajamas unless we're sick or something. That may or may not be something you have any control over.
Otherwise, if you know you're going to need to leave at 2:00 to get somewhere start encouraging him to get dressed at least an hour before. Let him pick out which shirt he wants to wear (or pick between 2 shirts), make it a game to see if he can get dressed before a timer you set goes off.
If push comes to shove and you absolutely must be somewhere and he refuses to get dressed, keep in mind that he's three. You are bigger and you can dress him. He might fight and pitch a fit, but I'm going to guess it's not the first time he's thrown a fit. Telling a 3 year old that he won't get to go do something fun when he's all ready having fun running around naked isn't usually going to motivate him to get dressed and go do something else even if you know he'd enjoy it, too.
He might grow out of it--he probably would--but he might be 4 or 5 before that happens. At some point something is going to necessitate him getting up and getting dressed on a regular basis (school, for example). Plus, at age three, now is a good time to start working with him on learning to dress himself. Once he masters that, he might be more inclined to wear clothes.