I found a solution! The following instructions will allow you to format your citations differently from the main text in Word. Even after Zotero (re)inserts the citation. It will prevent Zotero from overriding or resetting the styles applied to your citations.

(This works in Word 2016 for Windows 10, but I suppose it would do so as well for Mac)

To do this you will have to create two new Word styles. One for the citations, and one for the main text. In our example we will have black text and grey citations.


Making two new styles:

• The Citation Style
  
  
  1. Press Alt + Ctrl + Shift + S to open the Styles window
  
  
  2. In the bottom left corner select the "Create a Style"-button
  
  
  3. Name the citations style, like Grey Citations Paragraph
  
  
  4. Now you'll have to select Paragraph from the drop down menu as your Style Type
  
  
  5. The style can be based on any you like, but you probably want to go with Standard
  
  
  6. As the Style for following paragraph, you want to select the Grey Citations Paragraph (or your alternative & cooler name)
  
  
  7. Underneath you can format the text whatever you'd like your citations to look like. I will simply change the automatic colour to something grey
  
  
  8. After changing the formatting to your liking, press OK
  
  
  9. Keep the Styles window open
  
  


• The Normal Text Style
  
  
  1. Again: In the bottom left corner select the "Create a Style"-button
  
  
  2. Give this one a plain name, like John or Inline Black
  
  
  3. No you'll have to select Character
  
  
  4. This will grey out the last drop-down menu (Style for following paragraph) making your life easier!
  
  
  5. In the one but last Style based on field, you will probably want to stick to Standard
  
  
  6. Underneath you can format the text whatever you'd like your normal text to look like. I only change the automatic colour to black
  
  


• These two newly created styles are the foundation of this work around. Creating them was the most difficult part.


• How to use these styles
  
  
  1. Whenever you start a new paragraph after a heading -- or text that had a different style -- or in a new document, go to the Start tab in Word
  
  
  2. Before you start typing, you have to select your Citations Paragraph style from the Styles frame on the left side of the ribbon
  
  
  3. Type a few words and select the whole paragraph with your mouse
  
  
  4. Once that is selected, return to the Styles frame and select the Inline Black style
  
  
  5. If you selected the whole paragraph earlier -- that happens when the highlight of the selection goes beyond the last character -- whatever you type now will come out in black
  
  
  6. Whenever you click on the Add/Edit citation button in the Zotero tab and insert a Citation, the citation will be formatted in the Citations Paragraph style instead of the Inline Black one.
  
  
  7. Repeat this after every heading or text element that has a different style.
  
  

This should fix it. All the new citations you insert, all of them will automatically -- until you add a new heading -- be styled accourding to your predefined Grey Citations Paragraph style. This style can be always modified later on.

In case of a footnote, you probably have to change the default footnote style into what you want your citations to look like.

Apply the "Inline Black" style to the normal text.

You might have to re-insert your citation. This workaround only works for newly inserted or "changed" citations.

So you could edit your citation, change nothing and re-insert it.