<p>In .NET, if a class contains a member that is a class object, should that member be exposed as a property or with a method?</p>

Property. A Property is basically just a 'cheap' method. Getting or setting a reference to an object is pretty cheap.
Just to clarify, properties are usually supposed to represent the internal state of an object. However, the implementation of a member as a property or method tells the user how expensive the call is likely to be.