Actually, it's best to leave it uncovered. Natural rainfall is beneficial and moisture is necessary for composting. During dry seasons, some people actually have to water their compost piles to keep them working. They'll also shape the pile into a sort of bowl shape to collect the rain that falls. It's rare that a season would be too wet for compost, but in some cases gardeners will mound up their piles in the middle so they'll shed more water than they absorb. Critters aren't usually attracted to the decaying plant debris in compost piles. It might be a good idea to bury the kitchen scraps you might include--coffee grounds, egg shells, fruit and vegetable peels. But animal troubles are rare.