How to save node text and comment text to session or cookie while typing This site does a great job saving the text input even when a question or answer hasn't been posted. 

Is there a similar feature available in Drupal?
There was by crell: module Autosave. Not ported to d7 though.
Here is a quote about it (from the module's project page):

...  automatically saves a snapshot of your content type form using AJAX. If the user's browser or machine dies while editing a node; the edits will be presented to the user the next time they return to the node. The user may toggle back and forth between the last saved version and the version with the edits that were lost and select which of these they would like to continue with.
How often a form is autosaved as well as which content types to enable autosave for are admin configurable.