Extremes in the weather always brings out the worst in batteries and their connections. Don't matter if'n it's extremely hot or cold, either condition will exaserbate a weak battery, a loose connection, a corroded connection or a combination of all three.
A weak battery will fail under either equally but will seem to operate properly in mild weather.
As has been posted, make sure the battery is fully charged and that all connections between the battery & starter/solenoid are clean & tight. The clicking means power is getting to the solenoid but not through it to the starter terminal.
And a clicking solenoid sounds like either a weak battery, a bad connection between the solenoid & battery, a bad ground, a bad starter or bad solenoid contacts. It is easy to by pass the solenoid to see if the starter will turn over but you need to use caution as the current produced by a fully charged battery can weld metal! Not to mention burn your hands or damage your electrics.
Generally a 40 month battery is good for 40 months, a 50 for 50, a 60 for 60 etc etc etc. Anything over means you're getting your moneys worth but is also pushing it past it's time.....
Good luck
Volfandt