We need to agree on a definition of the soul, or at least an observable aspect of it. I would say that one such aspect is having feelings.
Judging by this aspect, the answer is yes. Seerah tells us they do. You may read about the story of the tree that felt sad when the messenger (PBUH) left it. The story and hadith are in Arabic here: http://library.islamweb.net/newlibrary/display_book.php?idfrom=71&idto=71&bk_no=118&ID=77