Calling a mini a 'miniature pony' annoys me too.
I also was asked, back when two of our mini mares had 2 and 4 week old miniature mule foals, why the 'tiny donkeys' were following the 'poor ponies' around. I explained that those were their babies and the lady goes 'Ha, I'm not that stupid, I know ponies can't have donkeys.' I then told her that the babies were actually crosses between horse moms and donkey dads, and that they were called mules. She rolled her eyes at me, told me not to treat an adult like her with such idiocy, and told me there was no such thing as mules and they were only in books.