Do you believe Grace told Horace that he was not Barbara's biological father in "Roman Fever"? Justify your answer.

While the text doesn't tell us, I believe Grace Ansley never revealed to her husband that Barbara was Delphin's daughter. I believe this for two reasons: first, Grace and her husband seem to have gotten along without a ripple of excitement or unhappiness. This is not consistent with a man finding out after the fact that the child he is raising is not his own.
But more importantly, the text emphasizes that Mrs. Ansley is a woman of few words. For example, we learn that she is "much less articulate than her friend." Mrs. Slade is the expressive one who does most of the talking. Grace Ansley, in contrast, is self-contained and tactful. For example, when Mrs. Slade wonders how Grace and Horace could produce a child as wonderful and vibrant as Barbara, a very catty comment, Grace holds onto her composure:

But her small profile was almost expressionless. At length she said, "I think you overrate Babs, my dear."

Since she is given to understatement and keeping her thoughts to herself, it is unlikely, in my opinion, that Grace told her secret to her husband.