2002 Jeep Liberty Renegade started car this morning very cold cold Car started rough now the engine is making a clicking noise

oxygen sensor?

Time for a code check.

check engine light flashing on/off on 02 jeep liberty what can cause this problem

You always check transmission fluid with it running and in park,If your dip stick has a place on it for cold use it cold,Other wise it should be on the full mark,you might want to look under your jeep for any new leaks!

It sounds like you need a new battery. If it's a 2002, then it's probably on it's second battery already and due for a new one. The clicking is the starter solenoid trying to engage the starter with the flywheel. If the battery can't supply enough "cold cranking amps" or "power", then it makes that clicking noise.

See that? Every once in a while I'm right!!! Reason is that the starter draws far more than anything else in the car. Lights and radio can easily be run by an otherwise ineffective battery, but when loaded (starter draws a bit less than 200amps), the battery will fall flat on its' face! When you jump it, the car is running off the alternator and seems to be OK, till you turn it off again.

how low is your coolant?

You need to check your electric fan under the radiator cowl. That pull the heat away from the ac radiator. Liberty's have two fans. One Mechanical and one electric.