From what I know, you saw someone trying to singe their horse. There are very few proper singeing lamps left to do this properly and controlled. The idea is that during the winter, horses are clipped (to prevent them from sweating and getting wet and cold) At the end of January beginning of February, clipping is usually stopped, to allow the Summer coat grow in. However, little stray hairs (commonly known as cat hairs) can grown along the belly, legs, and face. The singeing lamp was used to burn these of and create a look of a uniform, smooth, shiny coat. Most horses don't mind a bit, they like the warmth, but like I said, the singeing lamp is a proper grooming tool. The fire is controlled by a damper, and there is a fine comb attached to the lamp as a guard/guide of sorts.
As far as pulling the whiskers, I would imagine it is uncomfortable or bothersome to the horse (it may very well not be) but that is done because if you've noticed with clipping, the whiskers grow back at the same rate, so you get that five o'clock shadow look. Pulling them causing the hair to grow back differently, at either faster or slower rates.
If you think that's weird, you should look into banging the horse - which is another old technique used in grooming.