In my experience, there are two definitive issues with clippers - they don't like the sound, and/or they don't like the vibration. The sound seems to be the biggest one.
My girl is a little weird. I honestly don't even remember how I trained her to clip. But I can walk up to her in a pasture, and clip her bridle path and all her whiskers without her moving. I know she must have disliked it at one point, but it's so long ago, I don't even remember what I did.
However, our riding partner has a 4 year old pony that HATES clippers. The minute she hears the sound, or you get them anywhere near her, she starts violently flipping her head up and down. We tried several times, just rubbing them on her with them on, and she just freaked. I have Wahl cordless clippers, so I made sure the battery was full and simply put them in my sweater pocket, running. Then I just started grooming her and doing normal things with her, so the noise was associated with a good brushing, and natural activity. Within the same day, she permitted me to finally rub them on her neck, and even between her ears with them running.
Typically, once you get them used to the sound, you won't have many problems. I personally don't tackle whiskers though until they're standing quietly and relaxed for me to clip an entire bridle path. It's to easy to catch their muzzle if they move around and make it a bad experience. Heck, my Arab mare doesn't move and I accidentally dinged the corner of her mouth (no blood or anything, just a pinch when I caught a "crease"). Thank god for me she's so forgiving
I don't bother with ears since I don't show, and the ear hair is so crucial to keeping bugs from eating them alive. If you clip ears, make sure you take measures (fly bonnet) to ensure the bugs aren't eating them.