According to the [snowball Earth](https://en.wikipedia.org/wiki/Snowball_Earth) theory, all of Earth froze over at least once (possibly twice) in the far past. However, Wikipedia says that there are opponents of the theory who state that tropical portions of the oceans were not entirely covered. These responses have been motivated both by sedimentary deposits (also used by proponents of the theory) and by computer simulations.

Is there any consensus as to whether or not the surface of Earth's oceans froze over entirely during either of the two main snowball Earth periods (~ 650 million years ago and [~2.1 billion years ago](http://en.wikipedia.org/wiki/Huronian_glaciation))?

To be clear, my question is about surface ice, not underwater freezing.