The link to local regulation of agriculture:
That is the one that applies to platted subdivisions.
And I am not telling everyone regardless of where they live that they cannot have poultry. I stated that right to farm laws do not necessarily give everyone the right to farm. Ohio does not allow everyone the right to farm. The Ohio right to farm act merely prevents farmers from being sued for nuisance violations like odor and noise. Under Ohio law you can have poultry on more than 1 acre unless you live in a platted subdivision. If you are located in a platted subdivision more than 35% developed the local powers can prohibit livestock. Sure the law could possibly be changed. It's going to take loads of time and money which most people don't have. Better off to try and change things before you attempt to get started in poultry rather than after you are charged with a violation. For most people it is easier and cheaper to buy or rent another property where livestock is allowed than to fight the system. I listed the circumstances in which the law clearly allows poultry. If the op wants to check with an attorney that is their choice. OSU has a good one that doesn't charge. Her name is Peggy Kirk Hall, her contact information can be found on the OSU extension website.
BTW, Canal Winchester cannot prohibit livestock on lots of more than 5 acres unless the whole place was sold with deed restrictions. State law allows livestock on lots of more than 5 acres.
Cities can permit poultry, Worthington allows 6 chickens as long as they are 50 feet from the closest residence. And Columbus does allow 4 chickens. And in most of Madison county you can have any livestock on 2 acres provided you are in a rural residential district.
It is safer to assume you can't have poultry until you get legal verification that it is permitted than to assume you can have poultry and get fined for the lesson. I was told by township trustees, former village officials, long-time residents, and the board of health that my birds were legal. I operated under that information for 8 years. Then I find out I am in a platted subdivision and poultry is not legal.
The op asked if anyone had experience regarding the keeping of poultry under township rule in a platted subdivision. I answered with my experiences and the opinion of several attorneys. If you don't like the answer it still is what it is. The link to the state law is posted above, ORC 303, if anyone wants to check. Townships and counties can clearly prohibit poultry on lots of 5 acres or less in platted subdivisions. The op can still check with the county planning or zoning dept to see if poultry is legal in that location. But the way ORC 303.21 is written the short answer is no. They can try for a variance if they wish. It's not a cheap way to go and you could end up making all the neighbors mad. You could get the birds and keep them on the low down, for years even. But all it takes is 1 complaint and the poultry keeper will be on here begging someone to take their chickens before the county comes after them.