I’ve been Christmas to NYE week twice, and no way would I want a car anyway. That is the busiest week of the year in Orlando.
We stayed on site, and spent a lot of time enjoying the resorts (BWV and AKL). The parks got insane busy, starting with Christmas Eve but after Jan 1 things slowed down significantly.
I’d just use Uber to get around, and a towncar or Uber from the airport, as previous poster suggested. You will spend much less, and not have to deal with driving.