Someone rather famously called them suitable only for theater impresarios but the Astrakhan overcoat collar was worn by Winston Churchill and the Duke of Windsor.
Astrakhan collars are generally found on double breasted Ulster style overcoats when they are seen at all. The Ulster is a predecessor to the polo coat and has many of the same features including sleeve cuffs. Like the polo, versions intended for city wear have flapped pockets and are beltless.
For me the Astrakhan question arises in the context of whether the Ulster style coat that is to be made from the cloth in the photo should have a fur collar. On balance I think not, but I am tempted and I need to make up my mind before Peter Harvey's visit next week.