For the winter, they are busy...?

[birgit33]

Can one rewrite this sentence "They are busy collecting food for the winter" like this : "For the winter, they are busy collecting food."

[Raymott]

Can one rewrite this sentence "They are busy collecting food for the winter" like this : "For the winter, they are busy collecting food."

No, you can't do that. It's not colloquial, and it tends to make the sentence mean something different - "For the duration of winter, they are busy collecting food". That is, "They are collecting food during winter" - which is not the original meaning.
Similarly the following is strange: "For charity, we are collecting money."

However, if you're making a comparison, it sometimes works:
"For Mary, I'm buying a dress, and for Peter, I'm getting a new tie."
"For the summer she went to Brighton, then for autumn she stayed in London." (Note this means 'during', not "in preparation for".)