My nickname is Doc, and I'm a sales specialist at Tire Rack. We are very fortunate to have our own test track and test cars from BMW and Porsche at our disposal. It's very exciting coming to work and knowing I get the chance to drive on just about every type of tire from twenty different manufacturers. Please keep an eye on my blog for my take on new tires, wheels and suspension components that you can use on your vehicle. Thank you!

195 55R16
Mixing tires with different tread depths and tread patterns can be problematic, but more so for handling issues (one pair of tires handling water or snow differently than the other pair). My guess would be that the used tires were making noise all along, but now that the have been rotated to the front is more noticable. Best way to fix this is to grab two more matching Dunlops as soon as feasible.
The XIce XI3 is in good supply in your size and has been a very popular option for Coopers !
The 235/60R16 tire size is 27.1" in diameter and your "stock" tires are much taller at 29.5". The smaller sized tire will cause issues with your speedometer and ABS, and would be much more likely to blowout in the event of an impact. We cannot recommend that size as a safe option for your application.
Thanks
At this time, we have not come up with any "snow" wheels for the new 991 chassis, but have the Michelin Pilot Alpin PA4 or Pirelli Winter 270 Sotto Zero in Porsche approved sizes (245/35R20 and 295/30R20) in stock !