"Base housing" is not a very precise term. There are actually a number of different legal categories for housing located within the boundaries of a base, and the the laws of search and seizure aren't clear for all of them.
To start with, there is the "traditional" base housing in which the U.S. military owns and operates housing located on federal land. Typically you don't pay rent, your 'landlord' is Uncle Sam, etc. Such property is normally considered within "military control" and thus the C.O. can authorize searches.
However, the US military has rapidly been switching to various forms of "privatized" housing. Here the law is not so clear. For example, the U.S. government leases land to a private developer. They serve as your 'landlord' and you pay them rent, etc. The housing may still fall within the geographic bounds of a "base" (i.e. within the fence), but is it under "military control" for the purposes of search and seizure? As far as I know there is no definite decision, but most sources seem to indicate that the courts will eventually require a valid warrant. There is one important caveat, however. There may be some clause buried in the fine print of your rental agreement that gives the government greater power.
Generally, the key question is whether or not a location is under "military control" and what the "expectation of privacy" of a person is at that location. The Fall 2004 Military Law Review has a lengthy article on the subject, if you are looking for a source.