Shaky idle in cold weather

Hi! My old SUV has idle trouble in very cold weather. It only has a problem after I slow down or come to a stop. I keep it plugged in and indoors at night, and I let it warm up for a long time. The fuel filter and pump were replaced a year and a half ago and fuel lines are not frozen, it is continuously getting worse. Air filter has recently been replaced.
The truck's name is indeed trusty rusty, and I know it has massive amount of miles. Any advice?
PS- it is an eight cylinder 5.3. Not a three cylinder 5.1. LOL.