Help please - very excitable horse!

Ok, so the story goes as follows:

I've been given a small Nooitgedacht mare to ride (there is a stud farm at the University that I am studying, about 40 or so mares). The problem is that she is very excitable, tends to run forwards at the slightest touch of the leg, throwing her head into the air and going sideways (with remarkable agility might I add). I'm trying to get her to settle down, establish a rhythm etc. but I'm finding it rather hard to work with her as she seems very tense, especially in the arena.

She's far more relaxed on outrides but schooling whilst on an outride is not exactly an option as the outide is through whither high blackjacks and other than a long 'gallop stretch', the ground is rather water-logged. Plus, there is a large ditch to be crossed which my mare is absolutely terrified off.

I don't know a lot about her history as she is new to the stud farm and I can't seem to find out much about where she came from. She's petrified of whips and crops, even just holding one whilst in the saddle, so I think she might have been abused in the past.

At the moment I'm teaching her voice aids to see if that might calm her down slightly and I'm hoping to start lunging her this weekend. But if anyone has any other tips, exercises etc. I'd be very grateful!

Lots of circles and I mean lots of them both directions. They will give you more control

I just did some reading on that breed of horse. Sounds like they bond really well with people. You might try creating that bond by spending lots of time with her just doing nothing. I think trust is a big issue with them. Once you have it they will do anything for you.
I agree when riding do lots of circles, serpentines etc. Do lots of ground work, yielding the hind/fore quarters, backing, flexing etc. If she is kept in a stall do some lunging to get the fresh off before you saddle up. Once in the saddle do more flexing before you head out.

My horse used to be super sensitive to leg just like that. I desensitized him, first on the ground by rudding his belly and girth area lots with my hands,
Then I would rub my legs along his side just while standing, at first he would jump around but by talking to him and keeping him calm he got used to it.
I then focused on using as much leg as I could when riding, he is now at the stage where I put my leg on and he relaxes and goes steadier!

Thanks everyone for helping!

Wild_spot, I don't think she's too sensitive to leg aids in general as she is fine on hacks/outrides. I think she overreacts to them in the arena because she is so tense but perhaps I should try what you suggested from the ground in the arena.

Vidaloco, she's kept in a pasture 24/7 with two other mares. I am trying to build a bond with her, I joined-up the other day but she seems rather antisocial, both to other horses and to people which I think might be because of her past. I wanted to play the Pat Parelli games with her but I think most of them use a so-called 'Carrot Stick' which she would be petrified of. Her ground work is very good, she's perfectly behaved. She stops when I stop, moves when I do, turns perfectly with just a touch on her hindquarters or backs up with a touch on her chest. I still think its something to do with her being so nervous and tense in the arena....but I'm not sure.

Brittx6x6, thank you. I shall try that out tomorrow when I go ride her again. Hopefully it works!