iCloud is giving me empty PDF files
I've had this happen to me when the PDF itself was corrupt. Just plain "weird" behavior including what you've just described - the download beginning, nothing happening, the actual file eventually showing up and being unopenable.

Some things to try, in no particular order:


Check the file size - it's possible you really did download a 0 byte PDF. What shows up under Size when you hit Get Info on the downloaded file? If it is 0, try downloading the link from another machine on another network (on your phone or another computer, perhaps). If that doesn't work, the problem is likely on the sender's side.
If the file is a substantial size (around a meg or more), the problem might be on the sender's end. Something you could try if you suspect the file is getting mangled, is to have whoever created this file compress it in a ZIP/DMG and send you that file. 
Try downloading an alternative PDF reader like the official Adobe Reader and see if that can open it. Perhaps there's something strange about this file that Preview doesn't like.
Another way to confirm if the file is completely corrupt or not is to open up Terminal, navigate to your download folder (cd ~/Downloads), and then run the file command on one of the downloads. (file myfile.pdf). This checks the bits in the file that tell your computer what it is. If it's a real PDF, you should see something like:


myfile.pdf: PDF document, version 1.6

But if you see:

myfile.pdf: data

the file is indeed unreadable. If you see anything else, the output will give you a hint as to what you need to open it.