There are minivans. We took a cab from MCO to our Orlando hotel and they put us in a minivan. If you go to the taxi area there is a podium right outside the door and someone will ask you how many people are with you and where you need to go and get you into the appropriate vehicle.
Just make sure you go out the right door. It is quite a walk from baggage claim and it takes patience to get to the right door, but there will be a sign over the door to let you know the taxi area is outside.