Before offering a suggestion are you burning diesel fuel or waste vegatable oil?

Many of the suggestions already posted are good to check as there could be some kind of mafunction between the pedal and the injection pumps control arm. For example with car engine very cold have someone press the fuel pedal to the floor. Does the arm on the injection pump move to the stop?

Or for some reason you have poor fuel supply issues at cold temperatures. It is kind of early to assume the injection pump itself is the culprit. Certainly it may turn out to be so. But some other things have to be eliminated first.

I could suggest a few tests as well. Yet if others are performing your car service I hope they know enough about old diesels. You could be just ingressing a lot of air for example when the fuel system is cold .