I have a document set and I added a choice option column to it. I also have a document content type for this document set. I added that choice option column to the document content type too. Is it possible to do something with workflows that when I change the choice option in the document set, the same column choice option which is also available in the document inside that document-set also change?
Look at Shared Columns in the Document Set contenttype. These are columns that will be inherited by all documents you add to the Document Set, and also synchronize changes from the Document Sets column and down on your documents.
Here is a guide of how to do it from the GUI: http://en.share-gate.com/blog/document-sets-making-your-metadata-shine
And here through XML / CAML: http://www.sharepoint2010blog.nl/2009/11/16/Provisioning+A+Document+Set.aspx
And just as some additional clarification to what Robert is saying - what you are looking for is exactly how Document Sets work. If you add your choice column to the Shared Columns of the Document Set, the column itself and the value you set at the Document Set level will be pushed down to the documents inside the Document Set.
And, in order for this to work, you do not need to add the column to the document content type. In fact, I have read (unfortunately can't dig up the link right now) that having the column on the document content type may result in disruption of the inheritance of the value from the Document Set.
So in short, to make it work: