I certainly see no problems or issues, in asking a farmer, if you can walk through his property.
The only issue i could see, is if you had a dog, that was off its lead, or a bit unruly, thats the thing that most farmers are worried sick about.
My philosophy, is to always be polite, and try and get a conversation going with any landowner, that's easier said than done i know, but it sometimes works.
I can remember three years ago, talking to a farmer in Northumberland, and once he realised i was very interested in his brand new tractor, we got into conversation for ages, he was a decent bloke, as most of them are.
I recounted how i had spoken to Joseph Cyril Bamfords son, in the Royal Welsh Show in Builth Wells, years ago, and he was dead impressed.
We parted on great terms, and all because i admired his new JCB tractor and i had been friendly and polite.
Being polite, for some people, is a thing of the past, but it goes a long way.