Eleanor Harvey, the manager for today’s show and a curator at the Smithsonian Museum of American Art, has participated in such demonstrations since her childhood. “Some of these kids grow up with real horses, and this is an extension of what they do,” Ms. Harvey said. “Some of us, this is vicariously what we would’ve liked to have done.”

A few entries vividly depicted models clearing a fence or maneuvering around a barrel (for “Performance” classes); others were presented sans accessories, judged on their condition and their appropriateness for the class’s designated breed. Nearby, a young girl used a fluffy pink makeup brush to dust off her Saddlebred’s flanks before judges descended.

Throughout the space, parents were draped in folding chairs, stranded without Wi-Fi or electrical outlets for up to eight hours. Among them was Brian Martin, 45, of Montclair, N.J., chaperoning his daughter, Ella, 13, and her friend, Cate Bates, 15. Back home, the girls share a leased pony named Leo, but in the world of Breyer they have entire stables of horses to themselves. Ella has around a hundred Breyers; Cate estimated she has about 250.

Here in the exhibition hall, their “show strings” were fanned out neatly before them on towels and Bubble Wrap. “This is one of our favorite weekends of the year,” said Mr. Martin, remarkably serene for someone who had been sealed inside a convention center full of young equine enthusiasts since sunrise. He told me that Ella saved her allowance all year for Breyerfest, toting a wad of crumpled $5 and $10 bills in an envelope along for the journey.

‘Horse internet’ IRL

Cate and Ella are intimately familiar with the horse-obsessed corners of the internet. Cate has her own Breyer-specific Instagram account, and Ella is an avid viewer of model horse YouTube channels. (Facebook, Cate explained, is more for “the older people” — she only joined when she had to create an account for school, after which she made a beeline for the many model horse enthusiast groups scattered throughout the platform.)

Both told me that, thanks to social media, they feel as though they’ve found their tribe of people who “get it” — not like in school, where Cate says her classmates sometimes “look at me like I’m strange” when she tries to explain her hobby.