Magic The Gathering: Draw and Play cards (Keep Watch)?

An instant can resolve at any time, before the combat damage step in this case. An instant can also be cast whenever the caster has priority (instants can have priority at any time.) Keep Watch affects the draw of Snakeform as instantaneously as Snakeform can affect said creature before it deals or receives damage.

In other words, Snakefom can resolve before damage is assigned (combat damage step) even if the caster received the card in response to another instant triggered in an other step in the combat phase.

In not so many words; yes, yes he can.

The combat phase uses a number of steps. The last of these is the "combat damage" step, which is the only time that combat damage is assessed. If you opponent chooses to do anything to your creatures that affects the amount of damage they would deal before that step, then yes, it works.

Basically, it doesn't matter that your opponent drew the new cards as a result of Keep Watch. S/He can still use them like any other spell, provided they don't allow combat damage to be assessed before attempting to change the creature.