I have a bit of an obsession with making female animals orgasm. I've had varying success on the individual level but had fair success between species. First prize is an orgasm with penile penitration but that is typically dependant on size/anatomy. The correct pressure (less is more for the clit), cadence, motion, lube and location be it fingers or an arm is key. My tongue cramps too much for prolonged use but sure makes them melt.
For dogs and mares I like to rub the clit(glans) through the hood as my fingers are too rough to stimulate it directly. That's normally enough for dogs, and the climax is quite subtle.
Mares climax easily with fisting but not that rough violent nonsense. Make sure your hands and arm are washed and clean, fingernails trimmed short.
Foreplay with the tongue gives her vagina and vulva a chance to loosen up and the juices to start flowing especially if they are not in season. The vulva should elongate and clit will swell when they are ready. I then form a cone with my fingers and slowly push my very well lubed arm into her. If she pulls away during insertion I relube and try again slowly, only once, but stop if she is not comfortable with it. Trust, respect and consent is important.
If she accepts your advances she'll stand and maybe widen her stance and lift up her tail up. You may need to move her tail hairs out of the way. A gentle and slight twisting motion of the arm helps with gliding in. If you can feel her vaginal walls sticking to your skin, lube up more.
Once fully inserted I apply slight pressure using the blade of my hand in a fist (the incorect one that breaks your thumb) as the bludge cushions nicely and keeps finger nails tucked in. I sweep it rhythmically with a bit of downward pressure backwards and no pressure forwards above the bladder, close but not against the cervix in 6 inch sweeping strokes. Speed starting at a stroke every 2 seconds and increasing. You know you are doing it right when she starts to squeeze you arm, pushing it out slightly, squirting and grunting. Her ass will start bulging and let loose a few farts and queefs (if she is really loosened up). At that point you can speed up to almost 2 strokes a second to ensure you take her all the way. You know you are done when she pushes your arm out forcibly while pooping herself and the water show hits its peak. The grunts and farts are loud enough to wake the neighbors. At this point its best to give her a chance to catch her breath and bathe in bliss untouched for a few minutes.
Clean her up with a damp towel and give her a treat and a hug.