This article is from the Car Audio FAQ, by Ian D. Bjorhovde (firstname.lastname@example.org) with numerous contributions by others.
The following applies to all speakers in extremely cold conditions, but
the question most often occurs in reference to subwoofers.
The suspension of the speakers will stiffen considerably at very cold
temperatures (lower than 30 degrees F). So will certain cone materials
which may become more brittle.
If a very cold speaker is played very hard there is a small potential
for damage because more stress is placed on the cone's neck. The
likelihood of damage is minimal for well-constructed and well-designed
automotive speakers, however.
Thermally, the danger is minimal because the ambient temperature and
the coil temperature are so low that it is highly unlikely that a coil
will overheat and burn, despite limited movement and ventilation.
At temperatures between +20 degrees F and 0 degrees F, it is a good idea
to play the system at a moderate level until the car's heater has warmed
the vehicle interior. As the speakers warm up, they will play louder
and lower signifying that their suspensions are warming up and returning
to nominal compliance.
If the temperature is extremely cold (less than 0 degrees F), you should
avoid playing the system at all until the vehicle interior is warm.
This is to avoid stress fractures in the surround material (especially
with rubber surrounds).