Enthalpy mainly depends on the heat capacity of the system, which is an extensive property, rather than the temperature. Therefore, enthalpy too is an extensive property.

But for your question, I would like to tell you that it is not necessary that if a factor, say which is an extensive property of a system, should only be dependent on variables which are extensive properties. It may not. It can be defined by factors which are intensive properties of a system as well. 

Only thing you must understand is that what are extensive and intensive properties and how these are attibuted to any system.