You already experienced this problem if you are running dual boot like me. I just tried mount Windows partition in my Linux system but I couldn't create new file or delete some junk over there.
Windows systems has fast boot option in power settings and this is the problem why we couldn't write any data on Windows partition. Because this option holding disk alive. And if you create a new file or delete something on Windows disk it could be break down some things in Windows. Long story short, this is a security for Windows systems. But, we have options to make changes on the disk of course.
Try restart in Windows not shutdown. Yes, this is the solution for this. Easy right :) If you will shutdown Windows you will have the same problem. But, if you choose restart button not shutdown you can make changes on the Windows partition :)