I have been driving in winter weather for 30 years. First five years in northern New England and last 25 years in Colorado.
I still had major pucker factor when I foolishly thought it would be no big deal to drive an Audi I bought 14 years ago with the stock performance Z rated rubber.
At 20 mph on a very slight downhill grade with a very light dusting of snow the car ended up sideways and I almost took out a fire hydrant. It's a miracle I didn't hit anything.
Don't screw with this stuff.
Tesla is under no obligation to eat the cost of doing a home delivery but if they will do it for you, that's great... I would do it even if I had to pay for it rather than risking your 'precious' winding up in a ditch with body damage... which would be a sucky way to start your new car relationship.
BMW/Merc/Audi dealers deliver AWD cars with performance tires in the dead of winter all the time and usually they will have a plan to do this for the customer whether it is a complimentary home delivery of the car, loan of a set of all season wheels/tires.... etc.
Whatever you do DON'T drive it in the snow, especially for four hours.
Someone commented on increasing your following distance. I invite that person to drive on an icy road with performance rubber and discover that they have literally zero traction below 20-30F and become ice skates. You can give yourself all the room in the world to stop and still not stop.