I know a lot of people here on HC do. I think its cute! :) But yes, sorta ridiculous. I call Flicka my baby (to her face only!) But Sweet Pea is more like my BFF!! And Acorn's my handsome boy :)
I don't usually refer to myself as my horse's "mom", but i do ocasionaly call them "my baby" when im teasing my four year old about eating everything he sees. I see them as more of a best friend than a child, because i can tell them anything and i only have to worry about the other horses in the pasture finding out about it. In a way, were all like a giant family, but not by blood !
I'll call my horses brother or sister but I have never called myself their mom. In fact I call my mare mama since she takes so good care of me when I'm riding her.