2003 Dodge Caravan does not engage in gear

I have a 2003 Dodge Caravan. It sometimes does not get into gear, it stays as though it were in neutral. This happens mostly at start up in the morning. I have to push the gas pedal down far and hold it, revving the engine very fast and then it jerks into gear. This happens when starting the car but also a couple times after starting to move too. Especially if moving slowly (as in, through a parking lot) or coasting down a hill. Seems to happen with more frequency as the weather gets colder.