I've just had a response - although I should probably point out that this shouldn't be regarded as definitive advice. I'm giving you a rough summary of what I was told and I'm no lawyer.
As far as I can tell, it doesn't matter how the mud is deposited ie if it comes from cows then the rules still apply that you should take steps to do something about it. What might be different is that if it was on a very small road then the court might take a different view on what it regarded as negligence on the part of the farmer. ie it might say that an accident was 60% the farmer's fault because you'd deposited mud and done nothing to either warn people about it, or clear it up, but it was 40% the driver's fault because they should have been taking more care on that kind of road...
On a similar theme - I've heard people argue that if you put up a sign and then something happens you are admitting liability. I'm told this isn't really the case.
By putting up a sign you are admitting there is a potential problem - and if you do none of the other steps then you would probably be partially negligent in the event of an incident. But if you don't put up a sign but know the mud is there and it is a potential hazard you are actually making yourself completly negligent, rather than just partially negligent.
I think that is pretty much it.
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