If a picture is worth a thousand words, then this may end up being a novel, but I think it's better to snow than to tell. Plus, the graphics get more interesting as we draw closer to the winter weather event that will move into the region Sunday.
First, not a lot has changed since yesterday with the computer models still vacillating somewhat on snow totals, but coming to a consensus on timing. The key, as I see it, to snowfall amounts is going to be the ultimate track of the upper-level energy associated with this system, with a secondary influence from the amount of convection ongoing along the Gulf Coast. You'll see what I mean in the model solutions below. The surface low appears to take a track along or just south of the coastline of LA/AL/MS/FL.
Let's start with the computer model runs from overnight, two of which are depicted above. On the left, the NAM model, and on the right, the GFS. Not shown are the forecast tracks of the upper-level energy, but that is the primary difference between the models, causing the significant difference in snow totals. The track of the upper low is the favored position of heavier snow due to the associated dynamics and lift available. You can probably guess the track of the upper low in each model - the NAM takes it south of the metro area, thus forecasting only 1-2" for the immediate area, while the GFS takes it over the heart of the city and therefore indicates a swath of 3-5" totals over the metro.
I still believe (my thinking hasn't changed much the past 48 hours) that we will see a combination of the two above - a slightly more northerly track of the upper low (similar to the GFS), but with the gradation of the snow amounts that the NAM provides. I think we could see a fairly narrow (perhaps just 50-100 miles) swath of enhanced snow totals along the upper low track, which will likely set up over northern MS. A wider swath of general 2-3" totals will likely occur on the north side of the heavy band, covering much of the metro area including Memphis and Shelby County. This is similar to what the NWS has conveyed with the graphic below, though I think the upper end snow amounts depicted are a little aggressive.
I promised graphics, so here are some more that are interesting and support my position fairly well. The first (4-panel below) shows the probability of snowfall totals of 2" (upper-left), 4" (upper-right), 6" (lower-left), and 8" (lower-right). This supports the heavier swath occurring over north MS, but also a potential of fairly significant snow for southern west TN, where the Winter Storm Watch is currently in effect.
Finally, from the National Weather Service, their composite graphic showing (from upper-left to lower-right) probabilities of 4", 8", and 12" snow and one-quarter of an inch of ice. It shows a moderate probability of 4" of snow up to the TN/MS state line and low probability (but not non-existent) of 8". A significant ice storm will set up to our south across northern LA, central MS and AL, and into northern GA. Thankfully we'll stay cold enough to get all snow from this storm!