Also have a 2002 1.4i (AUA). Just passed MOT flying colours on emissions after I got the injectors cleaned and replaced the coil with a brand new Bosch one (having already replaced plugs and leads with Bosch ones) - it's running better now than at any time since we had it. Throttle body and EGR were new last year. Of those I believe firmly now the coil and the cleaned injectors contributed most to the massive improvement in running / lack of misfires although the other bits will have contributed significantly to the health of the engine. Worth having a look at your coil, particularly around the back of the casing as they do crack in places that aren't readily seen and that makes the likelihood of weakened sparks somewhat higher, especially in the damp (and especially further if the leads aren't in prime condition).
Does yours get worse when it warms up or at certain rpm or is it only on startup? Are there any other symptoms?
VCDS is a good shout although if the problem is just misfiring and cylinder shutdowns that won't necessarily tell you what the actual problem is. On ours to begin with there were EGR and throttle body errors that were fixed once the dead EGR and really dirty original TB were swapped out and re-adapted ; subsequently it was error-code free despite the uneven idle and mis-firey-ness around 16-1700rpm part throttle that suggested other stuff was going on. Finally a few weeks ago the misfire got worse and worse to the point of cylinder shut-downs (and was being picked up by the misfire counter on VCDS without a specific error being obvious) hence the suggestions here that injectors needed cleaning / servicing and I found the structural issues with the original coil and replaced this. Hasn't misfired once since and has been running markedly better (and more fuel-efficiently in my hands).
Re-reading your original post made me wonder if it is something to do with fuelling at the time when in older cars you might use the choke? Fuel temperature sensor?
best of luck, Robin