I daily drove my 986 in rain, snow, blizzards, etc for over 12 years. It's completely doable with snow tires, I recommend picking up a second set of rims so you can swap them yourself, and go with narrower tires. If you can find 16" rims those will work well in snow, if you go with 17's run 205/225 tires. Definitely get a hardtop if you plan to park outside, and make sure the drains under the convertible top are clear. Run the correct oil, I use Castrol Edge 10W-40.
Make sure you wash the underside of the car to get the salt off frequently. These cars where treated to prevent corrosion but Porsche only warrantied that for 10 years so you may want to assess for yourself.
All that said, if you absolutely you have be somewhere during a blizzard where there is more than 4" of snow (the base 986 has 4" of clearance) you may encounter issues. I would also suggest reading up on winter driving, and recovering from skids, rev-matching helps a lot in a manual. If you drive it like you stole it on snow and ice you're going to have a bad time, ask me how I know!
