Well actually it isn't, not even remotely. I was reading Pullein-Thompson Archive's excellent blog, in which the question of ponies in pony books dying came up, and that set me thinking. I think it's in DPT's Pony to School in which Seaspray, Pier's and Tilly's grey pony, dies of tetanus. This made a terrific impression on me at the time, as I can't think, offhand, of any other pony book I read as a child in which a pony dies, and I think it was a particularly strong bit of writing on DPT's part.
People are killed off, though generally before the book starts (Jill's father, Carmen's parents in Sheila Chapman's books). Heartland is unusual I suppose in establishing the heroine's mother as a character before killing her off in the first book.
There is of course Ginger, in Black Beauty, which in some ways I think is the least miserable of the deaths: you feel relief that Ginger's awful sufferings are at last over, although there is also the grief that she had to go through it all in the first place. Other ponies I can think of who die are John Steinbeck's The Red Pony - not a book to be read if you're feeling a bit under the weather - and there's Pamela MacGregor Morris' Lucky Purchase, in which the lucky purchase, who is old at the start, dies when the book is nearly over. This is another one that really affects me: the whole thing is treated very well, with the depths of emotion the heroine suffers suggested but not hammered home. The magic pony in Patricia Leitch's Jinny book of the same name dies, but I can't think offhand of any others by her. I have read a few Heartland titles, but can't remember if any horses die.
K M Peyton's race horse in the last of the Ruth series (Free Rein - but that might be the American title - apologies for not being able to remember the UK one) dies too.
My mind is a complete blank at the moment as far as ponies dying in any of the Pullein-Thompson's books go. Do let me know what else you can think of.
I'm interested in the whole thing I suppose because pony books are often accused of being poorly written genre fiction; and although some are, I think that's just as unfair as saying Ian Rankin must be bad because he writes genre fiction, when this is very far from the case. The best pony books don't shy back from tackling real life; or indeed, death.