It emerged this week that the 'Gotta Be You' singer had a three-month affair with the 32-year-old radio DJ last year when he was just 17.
Horobin has already tried to escape the revelations by taking a brief hiatus from her Heart South Coast show, but she has now exited Twitter as well after the band's fanbase gave her abuse.
According to The Sun, one user described Horobin as a "dirty pedophile" and said that they hope her marriage "rots in hell", while another accused her of having "raped" Styles.
An alleged friend said: "Lucy was having a few difficulties in her marriage and it just happened.
"She knows people will hate her for doing it, particularly with a young lad who is so high profile, but life is not always black and white."
Styles's relationship with Horobin is believed to have taken place before he started dating Xtra Factor host Caroline Flack, also 32.