2005 Corolla rough idle

Hi, I own a 2005 Corolla with 80k on it which I bought with 20k.
Recently, I've experienced rough idle during warm up and especially when
it is very cold out. This rough idle occurs whether the car is in
drive or park. Right away I thought it might just need some new plugs or
injector cleaning but I am not a mechanic so I don't know.
Has anyone else encountered this problem? The car runs just fine other
than this and runs normally when warmed up.