I think it's possible, but maybe not in the same way. You may not even realize it. I believe I have heart horse #2 right now, but it's such a different relationship.
My 1st heart horse was my first horse, an Arabian gelding named Victor. He was awesome, I loved him and we had a connection that was out of this world. I could climb on him in the pasture with no halter or anything, and I could ride him all over. I trusted him and he trusted me and we went through so much together. I had to have him put down 10 years ago and I still get teary eyed thinking of him. During the time that I had him, I got a little Arabian filly named Dora. I liked her a lot, but she was so showy and fancy, very fine boned and I wanted something built for endurance riding. It was maybe a year after Victor passed that I decided to sell her to someone that would show her and give her a chance with that world because I wasn't into all that. I had a few horses inbetween, still, none were special and none really clicked.
Back in 2008, a friend of mine was murdered. Not going to get into all of that, but I had a really hard time with it. Dora came back up in my life, and she was for sale. I don't know why, but I wanted her back. I REALLY wanted her back. I was afraid she wouldn't be the same (it had been nearly 7 years) but I scheduled a time to see her. When I got out of my car and started to the barn, she was tied out. When she saw me and heard me talking her ears pricked and her eyes got big and she went nuts, nickering, whinnying, prancing all around. The girl was like "wow, she has never done this", and when I got to her she smelled me all over and it was the same little filly I had owned the years before. Needless to say, I got her. She helped heal the hole in my heart from the loss of my friend.
I say all this because we do have a connection. She loves me with whatever love horses are capable of, she enjoys being with me and snubs most anyone else. I can call her name and she picks her head up and answers. Riding isn't the most pleasurable because I still want just a riding horse and she's very prim and proper. We have arguments, our relationship isn't perfect, but we're good for each other. It's in no way the same as my first horse, but the connection is there. It's like she and I are besties where as my first horse was my soulmate.