Download mail from last year?

Is it possible to download only recent mail, say from the last year?  Several people asked about this a few years ago, and it wasn’t possible then, but hope springs eternal.

Even better would be "all messages (with message body and attachments) from the last year, and headers only for the five years before that.

Same. I want to remove my outlook email client. But on my Exchange server, I have years of emails that I do not want to download. It’s dozen of thousouds mails.
How can i do ? 

Unfortunately that is still not possible.