would the performance pack differential aid in cold weather driving do you think?
It depends on the type of diff they fit... I haven't looked into it in any detail - all I've seen is that it is a mechanical limited slip diff
If it is a Torsen diff, then when you are under power in slippery conditions then you'll find that the car does not want to turn because the diff will lock, but that's OK because the Torsen diff only works under power, so get off the power, the diff will unlock and the car will turn. The Integra Type Rs, I had were, fitted with these as standard... They are fine to get you moving and once you learn that the diff releases when you're off throttle the diff works fine...
The rally car I navigate in (my mate's highly modified Skoda Felicia - now with ~150bhp 1.4 16v Polo engine) has a plate type diff and that's great on the slippery stuff it would go places where his Touareg couldn't
but these diffs need to be re-built every once in a while to replace the clutches and maintain their locking characteristics - so road cars do not tend to be fitted with this type...
I'm sure there are other designs and they will have their pros and cons...