It's important to know exactly what Right of Way it is - check on an OS map whether it's classed as a footpath. Dogs are allowed on here and the ramblers site you've been given is a useful one.
Your Parish Council will be your best option for tackling the problem, and it's likely they will have received more than one complaint if the farmer is in the wrong. Most PC's will have some kind of relationship with the local farmers over issues such as hedge cutting and maintenance of styles and gates etc so they may just be able to handle it with a phone call.
There was a huge thread on here recently about livestock in fields with Rights of Way. The farmer may have put the sign there whilst he had lambs or calves and just 'forgot' to remove it, or he may know that locals know better but is hoping to dissuade ramblers!!