Do Muslims truly believe in flying winged horses etc.?

Today I heard for the second time the statement by Mehdi Hasan that he truly believes in flying winged horses and similar incredible stuff because it is written in the Koran. I am not alone in doubting that Hasan is honest with regard to this point, it may very well be that he that he wants to keep up appearances as a devout Muslim. However, what else can we do than take his word for it? Then it follows that he must believe in much more horrible stuff that is in written in the Koran as well, which is a terrifying thought.

Hasan wrote a piece to defend his position. Amazingly, he writes in the usual apologetic way, using arguments that are have been shredded by people like Matt Dillahunty and Sean Carroll and others many times. Perhaps Hasan doesn’t care, perhaps he takes the position (also common among apologists) that it’s not his task to use valid arguments, but his duty to use arguments that appear convincing to people that still believe and need to hear that it’s OK to continue to do so.