The Snow? Well expect the very worst handling car in the world, They don't get going very easily, steering is atrocious and generally don't feel very safe at all, If you can get going and keep going then usually you will reach your destination, but stop anywhere with a slight incline and youll never get going again without a push.
I never had winter tyres so cant comment about what there like with them fitted.
I had two Boxsters over ten years and was my daily drive, no second car to rely on so whatever the weather I was out in it, fortunately we don't get too many bad winters that result in a great deal of snow so I only got stuck once, but even a light dusting of snow affected how the car drove and you always had some trepidation that you wouldn't complete the journey.
Running costs? - well unlike most owners I didn't bother with warranty, servicing - yes I had that done at indies simply to maintain the service history entries and the costs were no much more than an average car - £220 ish for a minor and £350 ish for a major - and its only every two years (But changed the oil/oil filter annually myself)
Brakes, pads/disks are quite cheap if you do the job yourself and buy online - all disks and pads about £450 - but rarely would you need to change all of them at the same time - Its usually the rear disks that seem to wear/corrode first on the inner face.
Tyres - cost is dependant on whether you go for "N" rated, premium brand and have a heavy right foot, exploit the handling of the car with P Zeros and the rear will be shot within 10000 miles - Mitchelin last a lot longer, Non "N" are a little bit cheaper - On the Boxster I really liked the GSD3s - not an expensive tyre but a fantastic performance tyre with a good life.
Lastly- the costs are dependant on how fussy you are with adding stuff to the car - most owners seem to chasing the next upgrade or really getting into the detailing world -Carnauba wax for instance - can be had for £25 a tub - or go for Zymol "Royale" and pay £7K a tub.
If you keep your car in standard trim, drive with empathy and occasional big licks, don't get sucked in to the upgrade paths and look after it the same way you would a mondeo then you will find the running costs surprisingly affordable.