Windows 10 won't recognize my Samsung Galaxy S6

I'm going to drop this in as an answer, since it solved my problem. Credit goes to beeshyams and Dan Hulme who set me on the path to see this.

The issue is an Android issue, not a Windows 10 issue. Apparently Android's new OS defaults to charging due to a perceived security issue. When you connect your phone to your PC, pull down the menu from the top of the phone (start at the top of your phone's screen and swipe downward). You should see a message saying that you are connected for charging:

Press on that message and you will see a screen where you can change how you're connected. On that screen, choose Transferring media files:

Now, if you go back to the first pulldown menu, you'll see you're connected as a media device:

Go back to your PC desktop and open File Explorer and VOILA! You can now copy your data to your PC.