In the summers, belly rubs are where it’s at for my mare. As I start currying her body, she will crane her neck around and sort of point her nose towards her butt like she’s hinting at what I should be doing. Then when I get by her back right leg - and only the right, never the left - she picks it up and will hold it out to the side as far as she can so I can scritch her belly, udder, and inner back leg (if I’m not enough paying attention and she’s super itchy, I wind up getting cow kicked because she jerks her leg up and out so fast that she gets me in the leg). I’m pretty sure if she could roll over like a dog, she would. She will stand there forever while I scratch as hard as I can - she particularly likes if I use the hard pointy end of the back of my brushes. I build in extra time in our pre-ride routine so that she can get a proper belly rub…it’s all about making the queen happy. She will sometimes do it while I’m riding, if we’re standing around waiting and someone is standing back by her right hind leg. She will just lift her leg up and look around for someone to notice and get to work. It’s pretty adorable.
However in the winter, you DO NOT rub the belly or touch the udder - that’s just asking to get yourself kicked. This is purely a summer time thing. Winter is for post-ride face rubs only.