I think that is because you probably did not install a full adobe application.
I have to do this frequently, and because I'm doing reports that are meant to be printed, the "click on the icon" option doesn't work well. The easiest way I have found to insert them, assuming you have a full version of Acrobat, is to open the PDF file in Acrobat and save it as a jpg. It will save each file as an individual jpg file (you might want to create a temp folder on your desktop or something to save them in). You can then insert several of these at a time. The quality seems much better than inserting PDF, too (I always find them blurry when I insert them into Word).
You can probably copy the text out of the PDF (Select all --> copy) and paste it into the word doc. Also check if you are in "print layout view" vs "draft view." You may be able to see the entire PDF if you go into draft view.
Press Insert>> object and then choose Create from File and browse the PDF files that you want to insert into Word. After this a PDF icon will show in your Word document and if you double click it, it will open.