I bought a pair of small battery powered clippers from walgreens (super unobstrusive and quiet). Every day, I would put my filly who was terrified of clippers on the wash rack and rub the clippers all over her while I was brushing her. I also gave her lots of treats. Then when she got comfortable with clippers while they were off, I turned them on and started to slowly clip a little hair on her neck, then moved to the jaw, then finally the whiskers. Once she realized it wouldn't hurt her she let me clip her. I did this over several months, and I made sure I did it every time I pulled her out of the stall. I would clip her even if there was nothing to clip! Now she lets me clip her ears and everything with the normal horse clippers. Just take your time!
I have done some desensitization with him, using the technique of showing him a scary object (clippers) and letting him back away from it and me while I follow him. When he stops I hide the clippers behind my back to reward him. Consider that he interprets this game as 'now I'm supposed to act scared' when she shows me something.
I got my horse when he was 7 years old and he had never seen clippers in his life so he was terrified. I trace clipped him for the first few winters I had him and for a few years, I had the vet come out and give him a nice cocktail. Never did I ever twitch him to do his head. I did as much as I could and each time I was able to do more. Now I can body clip him with no drugs whatsoever. I can also do his face and head. I think the cocktails along with not doing anything drastic like twitching really helped him realize he wasn't going to die :)