I understand that Adobe Reader is proprietary software, but it has well designed Search in Files functionality (accessible from Edit->Search menu or by pressing Ctrl+Shift+F).
Simple Search Options
The Simple search window is shown below:
You need to set Where would you like to search? to All PDF Documents in and then select location from drop-down menu (Browse for Location).
You can enter search item to the What word or phrase would you like to search for? field and specify search options: Whole words only, Case-Sensitive, Include Bookmarks, Include Comments.
Advanced Search Options
Advanced search is more configurable - see image below:
The search path is set in Look In.
Search item - in What word or phrase would you like to search for?.
Return results containing has options: Match Exact word or phrase, Match Any of the words, Match All of the words, Boolean query.
Other options include: Whole words only, Case-Sensetive, Proximity, Stemming, Include Bookmarks, Include Comments, Include Attachments.
Note: you can still install native Adobe Reader version 9.5.5 as described in other thread.