Shaveoff I'm still puzzled.
I've lived 10 miles from Newmarket for 62 years, know the town pretty well, for three years, until three years ago lived in Ashley Road, next road to Cheveley Road (which you mention) where I was right opposite a stud farm and Warren Hill gallops. Never noticed any horse muck in that road, nor anywhere. Are you sure you're not driving round the town looking for it?LOL
One of the roads you cite is in Exning, a village the other side of the A14 which acts as the Newmarket by-pass, not in Newmarket at all but what, 2 miles out? Of the others, not sure why anyone would ride down Doris Street, a short right angle of residential street.Birdcage is a bit more likely, though not very as to why you'd take a string of horses down it (you might in the adjacent road).Exeter Road, I take it you don't mean the end near the centre, but it may be that the rest is or was a bridleway as well as a public road (not sure , from memory, what condition it's in as to tarmac or road surface)None of these are in the centre of the town.
Are you new to the town (or to horses) ? If your a born and bred town person you'd notice one single drop of muck as some nuisance. (but you'd have no right to complain)As I say, I've never noticed muck as anything like problem. If you wanted muck on the road you could come to my village, where people do ride horses and ponies through the streets ! There there's more in one weekend than I've ever noticed in Newmarket (but we don't and wouldn't make a fuss because it's natural and part of living in a village out here)