Your problem sounds just like the one I had for the last year.  However,
mine had nothing to do with outdoor temperature.  Did you have this
problem last winter?  If not, it may not have anything to do with the
temperature, just coincidental that it started misbehaving in winter. 
Mine acted just like yours after driving for around an hour.  Ran
perfect on short trips in town as if nothing was ever wrong with it. 
After many parts replaced, it currently works perfect (fingers crossed
here).  I'm still not certain if my problem has truely gone away.  But
I'll discuss it further with you if you think it might help you.  The
list has heard all about it as I've complained and asked for help for
the last four months.  As far as what the first VW shop guy told you,
yes there is a problem with driving for a while and the engine missing
(not related to temperature), but VW DOES have a fix.  I don't think
that the fix would help, but you never know.

For the record listees, coolant temperature sensor seems to have been
the culprit (with air in the coolant system a momentary set back after
the new sensor installed).

Let me know if you want more info.
Tonya
87 Vanagon GL Wolfs
74 S. Beetle