Yep, I teach them to stand tied first. Once they have that down: I let them smell the clippers while they are turned off; hear them turned on from afar & then closer. I don't right away go to clipping, I let them feel the backside of the clippers while they are shut off. Then turned on. I usually do this right above the shoulder near the base of the neck on the side. And reach for baby and pull away quickly if they respond badly. It's the same as pull & release in rein training, basically.
Unless they were going to a show, I only did a basic body clip, & didn't do the legs or ears (inside or out) or face. I let that come later on perhaps the second try on another day. Maybe just get one part at a time (per session). Slow & easy does it for babies. If one is just terrified of the whole event, I'd let it go until it matured more & trusted me more.
And make sure mama is very near by. I usually tied baby & mama right next to each other. Mamas generally don't care if they can see what's going on & touch the babies & babies get so much out of her nearness.
Oh, and I've never heard of foal clippers, tho some makes & models are definitely quieter than others. I think a #10 blade is fine for body clipping a foal. I couldn't imagine wanting to get REALLY close to a baby's skin, unless showing, then still I, personally, am aprehensive about it. But that's just MHO.