Tappets, with a T! Google search, there will be youtube vids etc of how to set. Use the rule of 9.
If it runs fine when warm, filters etc are probably ok.
It is normal for old diesels to run well when hot, even if a bit old and worn. But cold starting is much more difficult, especailly in very low temperatures.
Cranking speed is often a factor, an old battery doesnt give much juice on a cold day, a landrover will tend to take more starting than a Mazda.
Like he says^^^^^^^^, make sure the glowplugs are working. That sort of engine likes preheat,and a good spin over.