We use during to say when something happens, if it happens in or over a period of time.
We use for to talk about the length of time something lasts.
They went to Florida during the winter. – They went to Florida at one point in the winter.
They went to Florida for the winter. – They went from the beginning to the end of the winter.
She phoned me during the week to tell me that she was getting married. (referring to a point in the week)
We were in the cinema for three and a half hours. Not: …
during three and a half hours.