Your barn owner is right.
Choose about 10 hairs at a time. You want to be right in front of the withers. Then, grasp them down close to the neck, and pull in a quick yank, straight up. The little bulb you see on the end, that's what they need.
Its easy.

 

When I've "pulled" hairs for my horses, I didn't even have to actually pull. I just brushed their mane with a metal mane comb, right up against the base of the neck, and enough hairs with bulbs on the end were brushed out. Tail hairs work too.

 

Some horses don't like having their hair pulled out and will react to the pain--so be aware. I think @egrogan's method sounds better and safer.

 

What could I use aside from a metal mane comb? I don't have one of those. I have a metal scraper thing that's supposedly not supposed to be used on horses but I use it very gently to get off dried mud. I also have a plastic mane comb.

My SIL brushed his mane out this weekend and apparently he didn't object, so I'm thinking he's not going to be sensitive.

 

The plastic mane comb might be enough or maybe a metal flea comb like is used for dogs and cats? I just know a horse who became high headed and anxious after having his mane pulled and he never got over it. Every time you went to brush his mane or halter/bridle him he would throw his head up after that.

 

Just give it a try with the brush you have- the roots/bulbs are really obvious when you are looking at the hair, so you'll see if it worked. And if he doesn't seem to mind, just use the pulling method you described. 30 hairs aren't really as many as it sounds.

 

When I did Minnie's DNA test - I did the same method as your BO suggested - BUT, be very careful once the hairs are out. Touching the bulbs of the hair can ruin the test. The Morgan Association had me tape the hairs to piece of paper and fold the paper to ensure nothing interfered with their results.

 

I prefer tail hair and I just grab about 20-25 hairs, wrap around my fingers and walk backwards and off to the side. You can do that a couple times and I've yet to have a horse 'complain'. I actually do about 20-25 hairs at a time and do it twice and I've never not had enough sample.