What would happen if you tried to "free lunge" her in that little pasture? I mean if you go out there and with your body language and maybe a stick or whip, you tell her, "time to move!" and you basically chase her around the arena, will she go? Can you move her by your body language alone, or with the back up of a whip? If you did this to sharpen her up , you could go out and with a playful but brisk manner (NOT predatory) say, "Let's go!" "Come on!" "here we go!" and ask her to trot out, will she do it.? If you do this some, you should get her so responsive that you can get her to trot from an increase in your body language's pressure on her, and get a slow trot, to fast trot, to slow, to walk, to trot to canter . . . .etc. Practive moving her and changeing her speed. And don't wait too long for a response. If you pushed on her (body language, not actual push since you will never touch her at all) and she does't go forward pretty promptly, then take the whip and crack the ground and wake her up. Once she moves along with this game, then take the pressure off, when she turns to look at you, back up and see if you can draw her in. Pet her and leave. She may actually enjoy it, but be prepared for her to kick out or jump . It's just a game but it's also experiementig with your being able to bring up her energy with your energy. If you can do it on the ground, you will better be able to do it in the saddle.
IF the pasture is really muddy, may not be so good to make her go too fast, but of coures, that goes without saying.