The Census Clause (Art. 1 Section 2) requires "counting the whole number of persons in each State", so they don't count houses, they count people. There is a perennial question about their methods of counting: they use a variety of methods. Ever since there has been a census, the law has them counting people in their usual residence, and the Census Bureau has a page on residence criteria. There are problems pertaining counting people without a fixed address, and this may be addressed by using social-science technology (i.e. estimating the number of homeless people based on interviews and visits to locations where the homeless might be). People living in mobile homes communities would be counted as much as anyone else is counted (they have a mailing address).
The municipal liquor license law allows a municipality a population of not more than 10,000 to have a municipal liquor store. That same law says "A city which has established a municipal liquor store may continue to operate it notwithstanding a subsequent change in population", and "A city which established a liquor store prior to July 1, 1967, may continue to own and operate it". The law allowing municipal stores also says that
(1) in the case of a municipal liquor store that sells at off-sale
only, all items that may lawfully be sold in an exclusive liquor store
under section 340A.412, subdivision 14, or (2) in the case of a
municipal liquor store that sells at on-sale only, or at on- and
off-sale, any item that may lawfully be sold in an establishment with
an on-sale intoxicating liquor license.
I understand that Bemidji has a population around 15,000 but has a municipal store. The statute came into existence in 1985 (or earlier). The population might have been lower when the store was first opened, though it might be that the population was 10,949 in the relevant year. The law does not state what basis is to be used for this population qualification; it might be a US Census estimate.
Whatever is going on, it is unlikely that this relates to mobile homes.