Owner of a '97 SE here. Last winter, I had very little life left on the brakes and tires. Firstly, I ended up coasting backwards down a curvy road on a very steep, snowy hill (~40° incline). Secondly, later that night, I coasted sideways through an icy curve, past an accident and a police car. The cop and I just exchanged confused glances as I drifted by at about ten miles per hour. That was not a fun night.
However, now that I have new tires and brakes, I'm looking forward to a calm winter. In short, any all-season or snow tire — with tread — will do. Bonnies are heavy, sure-footed, front-wheel-drive cars. Just don't drive like an idiot, and rinse/wash off the sand and salt whenever you can.
2007 Pontiac G5
1999 Pontiac Grand Prix GT - Stock engine ate transmission.
1997 Pontiac Bonneville SE - Cammed engine ate transmission.