There are two parts to your question.
my question relates more to how did they get Corleone's men onto the premises so that they could cut off the head and plant it in the bed without being noticed?
This scene was one of the major scenes where Mario Puzo and Francis Ford Coppola wanted to give their readers/audience a sense of the Godfather's powers. Woltz was a movie maker, though wealthy, it would not be a stretch to imagine the Godfather's men were able to overpower Woltz’s security.
Francis Ford Coppola never shows or mentions in his interviews why he doesn't show the process. The scene was intended for us to fathom the feats Don Corleone was capable of if his offer was refused.
Secondly, from the scene where Don sends Luca Brasi to the Tattaglia’s to say he is not happy with the Corleone family, it leads us to think the Don is well versed in such plots and had the capacity to buy Woltz's security too.
Two main themes we identify in this scene are violence and punishment.
The way Mr Woltz is portrayed suggests to the audience that he is not
a nice man, and we draw this from his incredible wealth, and the fact
that he sleeps alone and has no one to share it with. From this we
conclude that what is done to him is a punishment. And we know that
those who punished have a violent ruthless nature, from the extremity
of the punishment. Other themes are Italy and rivalry. The Italian
music is a giveaway, to those who haven’t seen the whole film, that
the story may be based in or about Italian culture, and the severed
horses head suggests mafia involvement.
Woltzs’ character is hard to analyse in this short scene as we don’t
see much of his action. However, from what we are told, we get the
sense that he is a materialistic money obsessed man. He has an
obscenely big house, which, from what we can tell, he doesn’t share,
based on the fact he sleeps alone. We draw from this the fact he is a
cold hearted business man.
Source: The Godfather - Horse head scene analysis
Or was it the usual case in those days of 'do what the mafia says or become a casualty'? Was there any backstory to this?
The answer is YES:
They used a real horse head in the infamous bed scene. The production
designer made arrangements with a dog food manufacturer that used old
horses to give them the head of a horse that had been scheduled to be
killed. One day it arrived packed in dry ice and they had to scramble
to film the scene. -
Source: 10 Things You Didn’t Know About “The Godfather” Including the Horse’s Head Was Real!