No tire thats good in the summer will be good in the winter. All seasons are ok in all conditions. Winter specific tires have an entirely different rubber composition that stays soft and grippy under 40 degrees. Most all seasons are ok in the winter but do not perform nearly as well as a dedicated snow tire. Especially not when there is any amount of snow on the ground let alone cold temps.
You live in NJ. You guys have some serious winter weather. I think you should look into running a dedicated snow tire setup. Nothing worse than snow banking your car and doing a few thousand in damage cause it snowed an inch.
As far as low profile, I believe your tire size is a 225/40. Thats pretty low profile. I personally wouldn't run anything less than a 40 series.
I know it's already been mentioned but probably the best performance tire that does well in the wet and lasts a decent amount of time is the Michelin Pilot Super Sport. Not the PS2 or PS2A3 or anything like that, the PSS. That's most likely going to be my next tire as well. I live in Kentucky now but I'm from upstate NY. Im used to a ton of snow and while there isn't very much here, I still ran snow tires this winter from November until May 1st. Saved my butt the couple times it did snow here.
A second set of wheels can is a large item to store but snow tires are absolutely worth it if you live in the NE. Just ask
@Dar-Dar - I think he has several sets of wheels.