It would not be such an issue if the stuff to be burned was allowed to dry out so that it does actually burn, quickly and reasonably cleanly. Once the main fire has subsided it would be nice if the person in charge would then either shovel some soil over the remains or dowse it with water to stop the hours or smouldering that so often follows.
Incidentally, according to the guidelines on the BCKLWN website, a bonfire should not be lit (in the final hour) before dusk, (the wording on the site is rather poor), and a bonfire should not be allowed to smoulder (especially overnight). I guess that lighting a fire after 19:00 is often going to fall in that '1 hour'. I am not clear whether these are just guidelines, an outline of bylaws or of legislation governing air pollution generally.
http://www.west-norfolk.gov.uk/Default.aspx?page=23854#1993As to horse manure, I think that has been discussed before, but if it is from a commercial operation then it is surely commercial waste and therefore there will be specific and specialised routes for its disposal.
All of this could be addressed by allowing the waste to dry out thoroughly before igniting it, and then by extinguishing the embers as soon as the main body of the fire has burned out.