This describes how I got my filly w no prior training to calmly and willingly allow me to trim her feet at liberty. It is still a work in progress, but....
When I got my filly she was a stout 2.5 yo and had no training of any kind. She didn't willingly lift her feet, much less hold them up/let them be held. I had no one to hold her. DH can some how mess up holding a young horse for trim work, which I've just chalked off to the 8th wonder of the world.
I used cotton ropes to get her to lift her feet. That effort went swimmingly and she became very compliant about lifting them. However, getting her to willingly hold them up/be held for any meaningful period of time was a different story.
I found that if she had her face in a pile of hay she didn't care what I did to her within reason - unlike my mare, which has the prima donna "I'm eating" attitude. So, I picked up the filly's feet and worked on them for short periods of time as she ate her curds and whey, and eventually was able to do so for long periods of time. Not surprisingly, she didn't position her balance "right" for the foot I would ask for, so I worked on whichever foot she was balanced for. It was a bit trying to switch back and forth according to her "hoof positions", but I wasn't in a hurry. I praised her exactly as I would have under "normal" circumstance (no food) and I never scolded her, after all it was her meal time.
Every so often I would try working on her fronts w a halter and lead across her neck (the only real purpose the tie serves is to be able get her to reposition her feet for balance). She got better and better about getting a trim this way (w just a lead, no hay) until I was able to trim/clean/whatnot her fronts w no problem. I still do her hinds whilst she is munching b/c otherwise she tends to want to "come see" me with her front end, and in the summer heat that can get exhaustive. We will "get there". And, she still hasn't quite caught on to repositioning her feet on her own. I think she is a little slow at "getting that" b/c I have, essentially, always done it "for her". Minor draw back.
I far prefer to trim when it is purely the horse's choice to "be there" (i.e., at liberty). There is always a "way"....and this is but one of them. Of course, as always it depends on the horse's temperament and one's patience.