It is possible to search (and replace) paragraph styles, but you cannot search for character styles. Please add that feature!
I love the idea. (Even thought I already submitted it ;) )
I agree that it is a good idea. Search and Replace should let the user choose which kind of style to search for, not only paragraph styles.
In addition, I would appreciate if you could attribute a certain character style to a search string. If I remember it well, this was possible in MS Word, too.
*** Bug 95029 has been marked as a duplicate of this bug. ***
Frank comment #3, that would need to be a separate bug - searching first to see if already created somewhere.
*** Bug 34390 has been marked as a duplicate of this bug. ***
*** Bug 44801 has been marked as a duplicate of this bug. ***
Since searching for paragraph styles is already implemented, adding character style search shouldn't be very difficult.