The carbon will be used by the plants to regrow where the goats grazed. Goats turn grass into stuff and the grass will turn it back into grass. Net effect: zero

The carbon will be used by the plants to regrow where the goats grazed. Goats turn grass into stuff and the grass will turn it back into grass. Net effect: zero. The difference with mowers is that they turn fossil fuels and grass into mowed grass. Other organisms will turn the mowed grass into stuff (like the goats) and grass will turn this back into grass. Net effect: burned fossil fuels.