As far as I can tell the AI basically just has a list of cards and has access to all of them at once. But can usually play only 3 per turn and follow size rules etc. Some of their cards can be spammed and others have a 'only 1 per turn' modifier on them.
You can click the deck at the top right of the screen to see the full list of cards, the ones that are not greyed out are currently playable by the AI while others may only activate when you or they reach a certain size or if you're in neutral or other 'stances'