I've driven through 4 winters with Supras (two in my 88 n/a auto, one in the 84 p-type 5sp, and one in the 89 1j/R154), and have driven all of them on Goodyear Assurance TripleTread tires. If you're still running 16's, they can be had in the stock size (17's I just couldn't find a good size for them though), and will get you out of damn near anything if you're a moderately skilled driver. If your car has LSD, you should be fine to drive through just about anything. Case in point, it snowed heavily here in Wyoming once for about 16 hours straight. Got to work, parked, and worked for 8 hours. Snow piled up on my car, around my car, just about everywhere really... by the end of my day, my car had snow up to the Supra emblem on the hood. The guys at the shop were all taking bets on whether I'd even make it out of the parking lot (I was the only one without a truck). I scooped as much of the snow off my windows and hood as I could to see, and about 2' of space in front of me so I could get momentum.
It was a fun drive home, I was doing the work of a snow plow (literally had 15" of snow everywhere), but I made it home. Trickiest part was getting up the hill I live on (~15* incline), but like Canuckrz said, MOMENTUM IS KEY. These cars handle winter roads awesomely IF you are moving. Hell, I put my old, tired (nearly bald) drag radials on my car one winter storm too early this year (in late April, figured I was clear, argh), and still managed to drive home safely. Granted, there was a bit of my awesome footwork at play, but still, it is possible, just takes forever and a day to get moving. It might not be a bad idea (especially if you don't have an LSD diff) to put ~100lbs of sand in the back. I would suggest putting it in the back seat though, and not more than 100lbs, for two reasons. One being that the more of the car's weight is centered between the axles, the better it will handle, and two being that while weight will help get you going, it will hinder your efforts to slow down.
Good luck and safe driving (to all of us who have to put up with the white blanket of doom).
Forgot to mention, switched to the Continental DWS this year, because I couldn't get the Goodyears that I like in a 17" (going to be putting the ARZ brake kit on my car next year) that isn't excessively tall. Hoping they'll work as good for me as the Goodyears have been.