Retail companies did it too. I would love to have seen the Milky Bar Shetland, and the Heinz Beans skewbald, the Kerry Gold Butter palomino, and the Sugar Puffs pony.
Susannah also reminded me about the TV ad which W H Smith ran to publicise their competition in the 1970s. It showed a girl posting her form, only for a neigh to sound from the post box after she'd turned away. This does ring a bell, despite the fact that my sister and I were not supposed to watch ITV, which was the only source of TV ads in the 1970s. We used to watch it illicitly, one of us close to the telly just in case, ready to switch to virtuous BBC1, and the other with an ear cocked in case we heard Mama coming down the hall.
Pony Magazine got very cross in the 1960s with all the ponies given away as prizes: both in well publicised national competitions, and as raffle prizes (Kathleen Mackenzie's Prize Pony is about just such a competition.)
Lieut-Col C E G Hope, who edited Pony Magazine from 1949-1972, published this broadside from Glenda Spooner and Lt-Col R C Kidd.
Did this make any difference, I wonder? The 1984 competition made it quite clear that the pony wouldn't be handed out to just anybody:
"The pony will be awarded on the condition of the winner being, in the opinion of the judges, a suitable pereson with adequate facilities to care correctly and humanely for the pony and upon the consentof the winner's parents or guardians. Should the winer fail for any reason to conform wilth the above conditions, £700 in premium bonds will be awarded in lieu."
which made it pretty plain that you were not going to be able to sneak this one past your parents, or keep the pony in your garden shed.
I did find this very bizarre effort from 2007: a Barbie competition to win a pony for a year - a year? I investigated further, and it turns out you won lessons on the same pony for a year, and transport and riding kit. Not quite the same thing. The promoter said it was about "empowering girls" - it sounds rather as if this just taught them that things aren't necessarily what they seem, and what on earth happened after the year was up and the girl had fallen in love with the pony and then that was that? Goodness.
Presumably the winner of the 1984 Pony Magazine Win a Pony Competition met all the conditions: here is Fiona Dixon, lucky girl:
Unfortunately I don't have any Pony Magazines after this issue, so I don't know what pony she chose or how they got on.