CALL HIM MUDDY
(RIGBY PB [AUSTRALIA] 1980)
Reprinted in hardback by Rigby a couple of times.
SUMMARY: Robert longs for a pet of his own but as he and his father live in a caravan, he isn't allowed one. When he finds a wild brumby his father relents and lets him keep the horse, as it can live outside. But this is just the start of his troubles….
Paperback original and as far as I know not reprinted at all. Hard to find in Australia, extremely so elsewhere.