I would think this has more to do with the condition of the battery,
connections of wires, condition of starter and bushing than the weather.

My 88 2.1L, with the stock starter, will start in 15 degree weather with a
slight bump of the starter.  The starter is 12 years old and is working fine.
 The battery is about 2 years old.  All the connections have been cleaned.


<< 1) When starting cold in the morning,...>>

Old battery, undercharged battery (If you do a lot of stop and starts not
enough time to charge battery up.)
Poor connections at: battery, starter, transmission ground.
Old grease or worn out starter bushing or starter.
Ignition switch

Check connections on battery, starter, ground strap for corrosion and
tightness, check that battery is OK (FLAPS will usually check for free).  
Pull starter and grease the shaft end that goes into the tranny.  Have
starter checked (remove the solenoid and add some grease).  Check the
ignition switch.



<< 2) After driving a couple of miles, >>

The speedometer needle is moved by magnetic induction.  Remove the instrument
cluster and lube the speedometer on the back side with a LIGHT** oil or spray
(If the bottle has a long enough spray tube you would not need to remove the
cluster).

**When I first got my VANAGON I used too thick of oil and when I first
started moving the speedometer needle pegged.  I was able to thin the oil
with WD-40 spray and it worked fine.  I had a clicking noise at 50 mph that
the lubing took care of.

Put some light oil down the speedometer cable from dash AND from the O2
counter box.

Robert