If your thing is "the goat", then don't cover its face with grass,(#2 is out) and oversize the goat.
I don't, however, associate goats with well manicured lawns. but the goat is recognizable
Maybe keep the name logo with grass growing off it and the oversized goat is half finished, with the eaten part nicely manicured, and the part left to be eaten is overgrown.
The cuteness of the goat is good, as most husbands leave it to their wives to make the initial contact. The cuter the better so avoid a wicked looking goat.
#1 font goes very well with cartoon goat