For the most part, yes! If you told me "I'm driving to work today" or "I'm going to drive to work today", both of those imply it is happening in the future. If you told me, "I'm driving to work." I would assume you are currently (present) driving to work.
For the Christmas sentences, they both are fine, but I would switch "at" to "on", which sounds more natural.
We're going to have a party on Christmas (day). We're having a party on Christmas (day).
Hope this helps!