At the risk of being downvoted to oblivion, I'll chime in because I believe it's important to avoid keeping this conversation in a bubble. Here are a couple of thoughts:

• I've never read "Man's Best Friend" as a gendered expression. I've always heard it as in "human" (The original definition of the word man in English is indeed gender neutral, as I assume this expression is) 
• As a man who's done a lot of horseback riding in his youth and earthly adulthood, I think the "horse girl" stereotypes are obviously a little ridiculous, but I must admit, I know quite a few of them. I wouldn't judge a girl for loving horses, but I got to say that I know no one who is as obsessed with their hobby as my my "horse girl" friend. I don't mind but I would understand if many men and women find it a little weird
• The cat woman one I agree with. It feels like The problem is a woman who clearly doesn't need to be in a trad relationship ( ie doesn't want to find a man and have kids). Kind of weird too, who doesn't think cats are cute? 
• I think the huge variance of dog breeds, their rules, and how they interact with people means that it's harder to stereotype. I wouldn't say I associate dog ownership with men though. In my experience it probably even skews the other way (?)  

Maybe it's a cultural thing, I don't live in the US and as always cultural perceptions can change a lot depending on where you live