The Maremma Sheepdog is best kept outdoors, for a variety of reasons. One, it is used to being an outdoor dog from its long history of guarding sheep in European mountain ranges. Two, it has a double coat that serves to protect it against cold and inclement weather outside to the point where it even repels water. And three, it sheds during moulting season and all that hair can get in your house.
The dog typically sheds once a year at the beginning of the winter months. However, the bitches are said to shed more than that, usually at the beginning of the summer. If the dog is kept indoors, the shedding schedule can be altered based on the environmental conditions in your house. While it is not supposed to shed year-round, it might lose hair as the furnace kicks on or it comes into air-conditioning luxury. The best thing to do is to simply keep the dog outdoors, where it is happiest and where you don't have to vacuum loose fur.
Some breeders will warn you that this dog does need heavy socialization as it is independent minded and cannot distinguish well between visitors coming to your house for a social call and an actual threat to your household. If you do keep the dog outside, you will want to make sure it is behind a large fence and that it can't get out. You will want to maintain a good connection with the dog and play with it or exercise it frequently. Even so, this dog is a sheepherder and guard dog and really doesn't do all that well in urban areas, unless you carefully pick out one of the newer breeds that are being bred smaller and with more docile temperaments.
The dog should be brushed regularly to keep the coat in good shape. It doesn't need to be bathed as the coat is so durable it even makes it hard for dirt to penetrate and repels brambles. The Maremma doesn't have a doggie smell like other dogs and the coat repels water, so many owners won't even bathe the dog. It is used to being outside in all types of weather and just needs a little extra care during hot seasons when the coat is a heavy burden. It might lie in the shade and will happily lap up any extra water you give it.
The fur on this dog is long and the undercoat is very thick. When it moults the amount of shedding is excessive. If you don't want to deal with shedding, keep the dog outdoors and vacuum during moulting season. The rest of the year, the dog is said to shed minimally.