First, make sure that she isn't refusing to pick up her feet because she is in pain. If she is exhibiting this behavior in all four feet, she is likely giving you a hard time; once she is trained, however, refusing to pick up a foot can be a sign of anything from hip pain to a thrush-related tenderness in that area.
A few points that have helped me train the young horses here, and re-train the rescued:
- DO NOT GIVE UP. If you go into that barn to clean your horses feet, do not leave until you do. This can take, and I am not exaggerating here, hours the first time if your horse is as stubborn/new as you are describing. Try all the methods at one shot, take water, use the bathroom before, but do not give up until those hooves are in your hand. Even if you just pick them up, without doing anything more, that is a victory.
- Pay attention to your body position, and make sure you aren't in some way unintentionally threatening your horse. If they have eyesight troubles, this can be tricky.
- Work on this skill every day, with not exceptions. Don't ease off until your horse is behaving to your liking.
- Work on this skill in a comfortable way to your horse, which may mean alone or with other horses (for instance, taking her out first while everyone is still in their stalls waiting to be turned out). I recommend the former, because if she spooks or starts fighting you hard, or you get clocked, no one else gets upset, but some horses freak when separated and you want her calm.
- Make sure she's square when you start. If she isn't well balanced, she won't throw herself further off balance by picking up a foot.
- Try working in cross ties, and on a single point. Some horses are more comfortable one way than another. If she's a fighter, do not work in cross ties - I've had green horses sit back so hard and fast they broke the ties or their halters, which was a blessing because the other option is their neck.
- Once you get the hoof in hand, if she starts thrashing or trying to forcibly take her foot back you must be firm, because you can really get hurt. To stop the thrashing or pulling, either give her a hard push in the side, in the "armpit" under the shoulder right where the girth sits (this is where horses nip each other so it is a responsive spot), and/or pull the hoof higher into their side.
- Reinforce good behavior with treats and pet.
- Work in the same order every day. For instance, I work counterclockwise from the front left. For some reason, they seem to do better if you work in a circle than both front feet, then both back feet.... I have no idea why this is, but it's a consistent experience.
- Find out what you can about her history. Has she always been barefoot or shoe'd, or could something there be throwing her off?
- Think about everything in terms of safety. One response mentioned leaning a little into the shoulder to shift the horses weight - I do this with horses I know and that are well trained, and it works, but I personally avoid it with the new or feisty. My experience has been that young or green horses will start to sway, or push their weight against you to regain their balance, which means you are then trying to hold up 1000 pounds or so.
Hope this helps, and good luck! Please do let us know what techniques work.