If my pup were magically turned into a horse, it seems that she would fit the role perfectly. Her mannerisms and body language are more horse-like than dog-like.
She really dislikes being handled. I can't pull her around by her feet, roll her over, slider her while laying down, get her out of the way by making her walk backwards.
I can pick her up fine with one arm under her rump and one under her shoulder/chest. She does very well with that... sometimes won't jump on the bed or couch and stares at me till I pick her up. I'm convinced she occasionally tries to fake injury cause that was the norm after she pulled a hammy once. I've been working on flipping her over just so she's comfortable with being handled. She really wants to flail midway through the flip, but it's getting better... especially now that she realizes a cuddle is coming up next. I often pull her legs just to get her accustomed to it. Not nearly enough to move her, but enough to get the idea across that it's ok.
She does not play like a dog either. My Chipoo seems to think that too and is very cautious playing with her (which is probably a good thing). He loves big dogs and can play incredibly roughly. It seems that he likes being the toy. She very rarely will engage in tug-o-war and when she does, it's brief. The Chipoo will get a couple tugs in then give up. He generally is very toy greedy (plays keep away) but completely gives up if she gains control of the toy. She will get a toy and forget about it once she has it. She doesn't play fetch. She finds where the thing lands, and that's the end of the game (pet emus come to mind... youtube it, it's worth it). If she is in an incredibly playful mood, she'll pick it up then drop it, but that's it.
The Chipoo is incredibly cuddly with other dogs, but not her. He usually will cram himself into another dog (that he knows), but he only lays close to her. He has no problem with her cuddling him tho.
The main livestocky thing she does is rub her face on people and things like a horse. That's how she cuddles people.
She did teach the Chipoo how to howl tho. I had no idea he was a howler. That's the most doggish thing I think she does.