Hi
It might make a difference whether you are trying to install the windows store app version of Spotify, Or the win32 Desktop program version downloaded from Spotify's website.
The Windows Store app version will install on the drive you have told Windows to install your Apps on[dependent on which version of windows you are using], you can change this setting in Windows 10 [1709] by going to:
Settings -> System -> Storage -> Change where new content is saved:
New apps will save to: and change the location to your (D:) Drive. and click apply.
This will change the location for installing all new apps from the store.
However if you install the desktop version from Spotify's website you should be able to set the installation location [and file save location] just like any other program.
As a side note, Windows typically likes a good 20~30GB free space on the C drive to give it room to breathe, so if you do not have that much space free, then you need to do some work freeing up space on your C drive, moving stuff to the D drive, and clearing up unneeded junk.
CCleaner from piriform might help with this.
If this has not been done already [and it sounds like it hasn't].
You can also, change the default location of your 'libraries' like 'Documents' and 'Music' and 'Pictures' which default to being on the C: dive but if you have a much larger secondary data 😧 drive they should probably be on that.
If you open up Windows Explorer [from the start menu or from the task bar] then you should see your libraries listed down the left side of the window. [if not you will find them in This PC -> C:\Users\[your username]\]
You can r-click on each library
Select Properties
Then go to the 'Location' Tab
And you will see that it will show your folder to be in
C:\Users\[your username]\Documents
for your "my Documents" as an example. If you create the Folder structure
D:\Users\[your username]
on the 😧 drive then you can just change the drive letter in each library you want to move from C to D and then click apply and it will both change the location and move all the files and folders across that are contained within that library.
Computers shipped with multiple drives should have this done by default as part of their pre-setup but it never is.