We have a footpath through one of our fields and some very friendly sheep and goats, but we decided to fence off the footpath so that the livestock are separate from them and any uncontrolled dogs. If they loose their hat or buttons though to the goats, from stopping to pet them, then I won't be help responsible!
One point, joking aside - you have to think carefully about signs you put up (sadly). For our pigs, we have a sign that says 'Pigs have teeth - please take care'. It doens't say 'Don't put your hands through the fence as there may be other ways of reaching the pigs we haven't thought of in advance (like them tunnelling their way out!) which would then not be covered.