It depends what you mean, entirely on Cloudfront.
Cloudfront is a CDN only. It can’t run any server side scripting environments (PHP or MySQL), it therefore isn’t possible to host a wordpress site entirely with Cloudfront.
You could alternatively use Cloudfront to host your images to improve speed. The closest way to host a wordpress site entirely on Cloudfront is to use ‘Origin Pull’.
It is relatively easy to setup (see this article), but still requires a backend server (therefore not offer a saving on cost).