yes zooming should be done entirely on your computer (like the normal rendering), but i'm not sure if it can be used afterwards to "increase your uniqueness"...

so this answer should also be relevant!

Update due to users comment and clarification:

to be accurate, you asked 2 different questions:

• If I change zoom level with Ctrl++, does it happen entirely on my computer?
  yes, zooming should be done entirely on your computer (like the normal rendering), but i'm not sure if it can be used afterwards to "increase your uniqueness"....
• Can I change the zoom level in tor browser (without affecting anonymity)?
  no, it seems that the zoom level can be used to "increase your uniqueness"!