If I understand your query correctly, there are two ways of doing this.
1- If you are willing to send the pdf file directly from "Document Cloud" storage via Hotmail email, then you may refer to the help document here and follow the steps suggested- Sharing PDFs
You just need to set up Hotmail email as a default email account.
2- If you are willing to get the file separately, which is saved on "Document Cloud" and then send it as attachment. Then you need to download the file from "Document Cloud" storage.
For that you need to go online- https://cloud.acrobat.com/recent download the file by clicking on the option shown in the picture below-
and then attach it to the Hotmail email from the location where it got saved.
Hope this is what you were looking for.