I agree with most of this but the definition of a bridleway is that it is primarily intended for use by horse riders, rather than just a way on which horse riding is allowed. Most UK bridleways are not suitable for riding a normal bike (not least because they often go through fords), but this is a multiuser path designed to be cycle friendly. For a map user, it is much more informative that this shows up as "cycleway blue" on the standard map  rather than "bridleway green".
