I watched an interview with Ernie Hudson and Harold ramis on Youtube the other day where they were talking about Ghostbusters. Ernie said that when he read the original script his character came in on page 6. When he was sent a redraughted version of the script his character then came in on page 40. He was really disappointed. Harold said that it was the management that made this decision and not the writers.
Personally I feel that it is understandable why Winston comes in so late in the original movie. They didn't need to employ anyone up until that point of the movie because they were not that busy to begin with.
However, I don't think that there is any valid reason as to why he is so underused in Ghostbusters II. By this time he is an established member of the team and unlike the first movie his character comes in at the beginning of the movie. He should have taken part in the investigation into finding out why oscars pram stopped in the middle of the street and the subsequent court room scene. He should also have had more lines and funnier ones too.