Hi Jessica, I think you're on the right track, as I'm thinking of something similar.

My friend had horses who all did that. As soon as she released them in the paddock, they took off bucking & whirling etc. and sending the dog into a frenzy, but my friend was very experienced and this didn't bother her. It was, however, behaviour that I wanted to avoid in my own horses, so (as our horses lived at the same place) I took a few measures to avoid it!

Sometimes the effort that our horses give to us while working can be more than matched by the enthusiasm that they show playing in the paddock! Just remember that she's not trying to be naughty, she's just excited, and she's excited because it's paddock time! If you can stop her thinking that it's "paddock time", then perhaps you can stop the behaviour.
Is it possible for you or someone to spend some time going in and out of the paddock? Mix it up, keep her guessing so that she never knows if it's "paddock time" or not. Lead her in the paddock, then lead her straight back out. Shut the gate. Maybe hop on and put the paddock out of her mind. Then untack her and lead her back in. But then lead her back out again! Repeat this practise until you notice her excitement reduce upon going into the paddock or until you run out of time. If you run out of time, do it again & again at a later date. It may take MONTHS, but if you're persistent, you'll get there!

Is it possible to do work in the paddock and then let her rest a while where her usual work place is?

Build up to leading her in there, pausing, making like you're going to remove the halter, then changing your mind and walking back out. Perhaps let her have something to eat when you take her back out?
When you do finally let her go in the paddock, be slow and steady with your movements. You probably just want to get it off as fast as you can, but be slow and calm, talk to her, and proceed with removing the halter when she's still, and if she moves, stop undoing the halter. She will eventually learn that it will be faster if she stands still. And pause at the end before you finally let her go, making sure that she pauses too. Like Monty says, "cause her to see the value in standing still"! See if you can't get her head to drop &/or take a couple of steps backwards before you finally release her to get her calm & thinking of something else.
Be sure to let her go at a different place each time you do end up letting her go. Make sure that you never place yourself between her and her mates though in case you get hurt!
Experiment with letting her go while she's facing towards the fence, towards an opposite fence, or towards the paddock. Remember, if she's not calm when you go to release her, lead her back out, come back in and try again.

You may have to put her other lessons on hold to focus on this one for a while, but it sounds like it'd be worth it, because you need to be safe! :) Wow, a long answer- I hope there's some things there to get you started (or at least the people who handle her)!

Hi, all good advice above Jessica :-) One method I used too was putting two headcollars on, undo the one she is not attached to and she will find she is attached to the second one - but please please use a long line and be careful when doing this. You can then put the headcollar back on, switch the line to that one, take the other one off and after a few goes one of the mares I was working with stood and thought for a minute as she wasn't sure if she could go or not. After two weeks of this she now stands perfectly still and waits to be released even after the headcollar is off. Good luck, let us know how you get on.

Wow, that's a great idea!

This problem has also been prevously discussed on forum so you may check it out via a forum search.

Thanks all, that is really helpful