I have been in the Mississippi
River on both sailboats and commercial
boats. Sailing north would be very difficult if not impossible. As READY2GO stated there are always currents in the river. If you were going north during the spring, you would also have the snow runoff (floods) to content with. Also the river is not wide enough to tack in especially given other river traffic.
Major corridors on the river have Vessel Traffic Service
. Having traveled in New Orleans
going up the river, I would not sail up the river.
Most people use the Tom Bigby
north then come down the river or east coast