Welcome (in advance).
As mentioned, a set of all-season tires would be better suited for the 9 months of rain we get around here, but I've run summer performance tires all year long before without issue. I've lived in the Seattle area for 30 years
I think it really depends on where you're at and/or if you plan to drive your car in the snow. We don't get a lot of snow here...an occasional freeze, and sometimes a couple back-to-back days of snowy weather which ranges anywhere from a dusting to a couple of inches to a whole pile, depending on how the storm hits. The snow and rain patterns around here are a little nutty with the convergence zone. But, it's usually all melted/gone within a week's time. The killer is the sand they lay down. When it freezes, Seattle sands (and now salts!) the roads. The sand hangs around and makes for a crappy mess, and cracked windshields and extra rock chips, if you're not careful.
I don't drive in the downtown Seattle core area when it snows. Hills are steep, and there's likely to be more than a few idiots sliding downhill, out of control, including articulated Metro buses. Also, there's this weird phenomenon where people just abandon their cars in the middle of the road when they can't make it up a hill or around something. :P
Your convertible top will be useful until about October. Then, you can be part of the elite breed of Washingtonians that drive their convertibles topless in 40 degree weather. You'll see 'em...occasionally we get a dry day or two in the winter, and these peeps are going down the road with the top down and heater on high, bundled up in a coat.
Anything else you want to know about the area, or about Camaro life here in pioneer country, feel free to PM any of us!