Yes mobile homes which are also known as manufactured homes are made to be lived in year round.
When people have a mobile or manufactured home delivered and setup on their property they typically never move it again because moving a mobile home is costly and usually cheaper to buy another mobile home instead.
Many people including my mother lives in a mobile home year round which is what they're made for.
My mother has lived in her mobile home for 25 years now and they're cheaper to live in and have cheaper real estate taxes than a traditional site built home.