You can do it. It's good that she's approachable and lets you pat her. Do you have a reasonably small enclosure to use? First you have to get the halter on her. Do you have a chute and headgate (the easiest way to get a halter on her without too much trauma). Does she come to you for feed? Give her a little grain or treat AFTER you get the halter on her (before releasing her from the headgate). You can also put a "sacrifice" 6-8' lead rope on the halter at that time..."sacrifice" meaning it will be dragged through mud and glop and probably won't last too long, but long enough for what you need to do.
She may jump and boink at the rope some, but not for too long; let her do this on her own time, without you on the other end of the rope. Be sure she has access to hay and water in the enclosure.
Next day, entice her into the smaller enclosure again, approach her with a pan of grain and when her head goes into the pan, pick up the rope and the pan (move slowly). Move the pan a few feet and tell her "walk" while you hold the rope. Keep doing that a few times. She'll catch on. After a few days of this, you can tie her fairly short, maybe a couple of feet (using a quick release knot) to a stout post in the enclosure. She'll fight the rope some until she figures out she isn't going to win (but she isn't fighting YOU). Don't leave her tied without supervision. Once she relaxes a bit, you can calmly and slowing begin to touch her all over (careful around the legs, they can kick in all directions very fast), brush her a little bit, give her treats, talk to her, then lead her around in the enclosure some more. It's easier to work with one if there are no other animals running loose in the same space because they'll interfere.
When I teach mine to lead, they have to come into the enclosure to get their grain or treats; if they don't come in, they don't get to eat it that day. With the rope on their halter, you have something to grab onto (but do it slowly). They usually learn very fast, and they don't forget either! And after a while, they give me dirty looks if I don't come across with treats and brushing; they like the attention. I teach "whoa" by walking them up to a board fence, a deadend. Usually, I do some leading (with the grain bucket), then tie and brush both sides for a while, including the face, legs, handle the udder, talking the whole time. Then I lead some more before I let them go. End on a good note and a treat, praise also.
Time consuming and all that, but it does work. Try to resist leading in a pasture until they're used to it cause if they pull away from you in a big space, they think they can do it all the time. And don't wrap the lead rope around your hand, no matter what; if they bolt, you could get dragged...no fun.
Sorry this is so long, tried to do it step-by-step; other people may have faster ways that work...this is just what I do. I have donkeys but have never used them for halter-breaking; although a tractor will work, I don't like the idea as it doesn't instill trust in you, the person. I would do the lead, tie, brush, lead routine everyday for a week, then at least several times a week, depending on the response from the heifer. Patience, perseverance, and praise...don't do it if you are in a bad mood or rushed.
You're right about the lead length...and some of them learn exactly how long that rope is and how far to stay ahead of you faster than they learn all the other stuff. The small pen helps cause there's no way you're gonna outwalk them in a pasture.
