This feature is now available on Spotify, you don´t need to connect Facebook to change your profile picture. Now you can change/remove your user profile picture:
1. Go to your Spotify user;
2. Click on your profile picture, it should appear change on the bottom*;
3. Now Remove or Change;
4. Upload the image you want;
*Make sure you're in your primary PC or Mac account. It won't work if you're
on another device in the app.