Rough Idling: EGR, Spark Plugs, or Thermostat?

Well, I have that 1989 Mazda 626 but it should be the same as a Honda.
Six month ago the engine was idling rough, dropping from 750 to 550
from time to time, and I get hiccups on highway. I brought it to the
mechanic, and he cleaned the EGR valve, which was like a plugged pipe.
The uneven idling was getting better, but not gone.

Couple of days later, I pulled out the spark plugs, and found 3 out of
4 have severe oily ash deposits. Changed the plugs and it got much
better.

Now I am wondering if a stuck-open thermostat could be the mother of
all these problems? Our temperature is hovering around 35 F and it
takes 4 or 5 miles to warm up the engine up to normal. I was also told
that my car has more white vapor than other guys'. So I am suspecting a
stuck-open thermostat. I just did not get a chance to pull it out.

So here it is: plugged EGR, fouled spark plugs, engine running cool,
and uneven idling. Is there some chicken-egg relationship between them?
Any comments appreciated.