There may be more complex issues to debate but ...
Section 3 of the 1991 Act created a new offence of being an owner of a dog of any type or breed which is dangerously out of control in a public place or a non-public place in which it is not permitted to be.
... might cover it. If we assume that any place where one might find a 4WD being driven, or a horse being ridden, is a public place, then it probably falls to the owner/s of the dogs to keep them under control. If that is the case, then I don't see why charges would be brought against any rider or driver who happened to be in the vicinity. Whoever has charge of the dogs would be the one to cop it wouldn't they?