Diesels don't run too rich.

If this engine has done 250K miles or more I suspect incomplete
combustion due to low compression; have the engine's compression tested.
Then you'll know for sure that it needs an overhaul, or not.

My '87 does the same thing. Does it more in cold weather, does it less when
using the block heater.
I think the valve stem seals are leaking lube oil and the combination diesel
and lube oil is producing the white smoke.
Or it could be as T.G. suggests-low compression. I haven't checked the
compression 'cause I'm not concerned about the smoke on starting since the
car has 270K miles and runs just fine otherwise.

You should know that if you don't let the glow plugs get pretty hot before
cranking, or if the car turns over quite a bit before starting, you are
going to have a lot of diesel fuel in the cylinder areas. Your car will
smoke after starting for a little bit until this extra fuel is either burned
or spit out the exhaust. I have a 240D that starts like a well tuned gas
engine but, if I instantly start cranking the engine without waiting for the
glow plugs to heat up it will blow blue/white smoke out the exhaust for at
least two or three seconds, even though the engine is running smoothly. How
long since you've replaced the glow plugs?

Incidentally, mine is an '81 240D with only 120k so that helps explain the
quick starts......oh yes, I'm also southern Cal.