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.
Ex. They went to Florida during the winter. ( They went at one point in the winter.).
Ex. They went to Florida for the winter. ( They went from the beginning to the end of the winter.).
Ex. She phoned me during the week to tell me that she was getting married. (referring to a point in the week).
We can also use for to refer to public holidays and seasons:
Ex. He always goes to his mother’s house for New Year. (Not: ...during the New Year).
**The words "During" and "While" are also confused very often.So: