Our character today is 户. Based on its current form, it is quite hard to believe that it has close relationship with 门 | 門. However with the help of its Oracle Script we should immediately know its original meaning. So let us examine its evolution history: (image taken from http://vividict.com)
|Learn one Chinese Character a day - 户|
Its Seal Script was added to emphasise the fact that door is made by wood. I guess doors were made of other materials along the time, was thus simplified back to , then slow change to and then to 户 as of now.
Below is a photo of what a 户 looks like in China:
|户 - Single Door|
|門 - Double Door|
While a poor or small family could only install a Single Door. That is why we say 小户人家.
That also explains the meaning of 门当户对：when getting married, if you have a double door house, then marry somebody living in a big house; if what you have is only a single door apartment, then you should marry somebody living in a small apartment as well.
As 门 | 門 is eventually dedicated to mean all types of doors, 户 is then used to mean Family or Household. But please do remember its original meaning while it is used as a Chinese Radical.
Now it is time for us to enjoy a Chinese calligraphy with 户 inside: