Frozen suspension in the winter
Disclaimer: I used to design and sell after market suspension parts for proflex bikes

There are three main strategies for the "spring" in fork suspension


coil spring 
elastomer stack
inert gas, e.g. air or sometimes something fancier.


Nowadays all springs are dampened somehow either by


using oil, 
negative air (opposing force on the spring)
friction (frequently used on cheaper elastomer stack forks)


Cold temperatures effect oil and elastomers but have no real affect on the other types of springs and dampers.  

In sub 0'C temperatures oil can become much more viscous and can't dampen the shock properly (oil is forced through little holes to slow down the spring-back of the fork) and thus make the fork feel like it is not responding.  If you keep riding, the friction might heat up the oil a bit.

Elastomers are harder to heat up.  I know Proflex riders in the nineties used to pour boiling water on the elastomers before going out for a ride.