Mounting to a specific location should not affect the permissions of the drive. But in the case of NTFS and some other filesystems, Linux is not compatible with their permission model, so it is simplified by e.g. making all files be only accessible by root.
You can override this default with mount options, or change the permissions to sensible values with chmod and chown, but I’m not sure if changing them will have negative side effects on the windows side so the latter may not be a good idea.
I would recommend to put them inside /mnt for internal disks. It’s a bit more organized that way, and by looking at the path is easier to know that it’s in an internal drive.