Yes! The Boxster is an able car to drive in winter months, even in the snow. Due to its mid-engine design which places more weight on the back wheels, the car can drive in reasonably snowy conditions. If the snow gets too deep, however, there can be problems due to the low clearance of the car.
Generally, the consensus is to use the original 16-inch rims that came on some earlier Boxster's. If you can find a set they are great in snow because ther narrower wheels cut through the snow instead of plowing it. 17-inch rims with snow tires are also effective, the choice is yours.
There are few tires spoken of most often:
I had the LM-22's on my '03 with PSM. Very capable in snow, ice and mountains in Colorado. Great for snow one day, and driving at freeway speeds the next. They work like magic :) No problem with noise. BTW, if driving in snow definitely get the PSM (standard on '05 and newer).
Well I have LM-25V on my 02 with PSM + 030 with 265.35,18 at the back 225,40.18 front. And were we are in Poland in the mountains they just are amazing. I have driven with them down to -22.5c Have now sold the 02 986 and got an 06 987 with PASM. It has Michelin Pilot Alpin PA2 205.55.17v front 235.50.17v rear, and it is even better than the Blizzaks were in the ice and snow here in the Polish mountains.