I am planning to run a cluster of Raspberry Pi Zeros. I know we can do it with a cluster of Pi 3 boards but I want to know is the same possible with Pi Zero?
It shouldn't matter if you use a Pi 3 or a Pi Zero in a cluster; functionally they are both single-board computers that can run Linux. Of course, you should expect significantly worse performance from a Pi Zero cluster than the same cluster using Pi 3s, because the Pi Zero is significantly slower than the Pi 3.
Remember that lots of slow computers in a cluster don't generally make one fast computer (unless your task can be run in parallel), so make sure your task is suitable before making a cluster.
But if you want evidence that it works, you can see this article (originally in issue 55 of the MagPi):
ClusterHAT is an ingenious solution to the problem of building a cluster computing. Learning distributed computing is something of a challenge, and this small hardware kit is the answer.
Our ClusterHAT review looks at how to build a cluster computer using a Raspberry Pi and four Pi Zero boards.
This uses a ClusterHAT which is specifically designed to run a small cluster of 4 Pi Zeros on top of a controller Pi.
Hackaday also give an example of a cluster which can potentially connect 16 Pi Zeros together on a bespoke board. As you can see, Pi Zero clusters are easily achievable, just like Pi 3 clusters. Whether they're useful to you is an entirely different question.