engine misses when cold on #3 cyljnder
And your question is?
Do a compression test and then If tune up is due, go ahead and tune it up. No lost money and it might fix it.
If it’s actually missing you will usually have a CEL on , read the codes and see what they tell you .
The truck is 20 years old so I agree; run a compression test on all cylinders. If compression is good then you might consider a faulty spark plug or even a partially clogged up fuel injector.
Injectors have tiny screens in them to act as the final line of defense against contaminants so maybe it’s just not allowing enough fuel through on a cold engine.
Again, compression first. If a cylinder is going down then it’s decision time.