Why does even the most rational brain forget logic in a dream?
Neither rational nor logical

&quot;...there is overwhelming evidence that Humans cannot be [rational]&quot; - Daniel Kahneman (Thinking Fast and Slow).

To begin with, the brain is neither rational nor logical as you may think (to a large extent it is little rational and its logic is completely fuzzy). A perfectly rational and logical organ would not be able to keep us alive (such an organ could take 4 hours to choose between two bottles of wine).
So I assume that your question is more like:

How comes dreams often involve augmented reality?

On augmented realities
Try this: shut your eyes and try to imagine your lower body replaced with that of a horse. Can you do this?

You have not done this whilst dreaming, but whilst awake and conscious.
Can you bring memories of a deceased relative whilst awake? Sure you can.
So the ability to experience augmented reality is not reserved for dreams - we can incite such reality by conscious means, certain drugs or brain damage.
Whilst you were dreaming
There are various theories on why we dream and what happens whilst we dream.
A key to many theories is random brain activity. You actually experience this whilst awake when you leave the central executive mode (stay-on-task) and enter daydreaming one - where short thoughts are following in what often seems as random.
Such random activity is fully capable of triggering augmented reality, like a half-man half-horse.
There is a higher likelihood for such augmented reality to appear in dreams, since random activity is not tamed by the stay on task mechanism.