You can never imwrite() a graphics object, including not even if it is an image.
Some kinds of graphics objects (such as images) you can pull out matrices of data that you can then (possibly process) and then imwrite(). You could pull out the XData and YData and UData and VData matrices from the quiver object and use tools from the Computer Vision Toolbox to recreate the quiver plot into an array. But that is a bunch of work.
What you probably want to do is use is getframe() the axes, and use frame2im() and then imwrite() the image that results.