Just take your sheep to the spigot outside and wash him once a day. You'll get Golden Wool pretty easily, even if you miss a day here and there because of rain. You'll actually need to wash all of your livestock once in a while, so get used to pushing those cows.
I only give Good Fodder to cows giving milk. It's not worth it for any of the other animals, but that S Milk, along with resulting Butter and Cheese, quickly makes up for the cost Good Fodder.