Who said "One bad move nullifies forty good ones"? This quote is attributed both to Bernhard Horwitz and I.A. Horowitz, and I'd like to know which one said it.

One thing that helps is they don't have overlapping lifespans. Bernhard Horwitz died in 1885 and I.A. Horowitz was born in 1907. We can probably safely assume that, if I.A. Horowitz said it, he had to have been at least 20 years old, so an attribution to Bernhard Horwitz from before 1927 should be considered reliable. Likewise, if no references to this quote before 1927 can be found, then it's probably I.A. Horowitz.

Alternatively, we might find a source that gives a more detailed attribution, such as "Bernhard Horwitz uttered this at such-and-such tournament" or "I.A. Horowitz wrote this in the January 1935 issue of Chess Review".

My hunch is it was I.A. Horowitz because he wrote for The New York Times and Chess Review, so he was a prolific author, so he had many chances to say something notable. Still, Bernhard Horwitz did write at least one book, and it does seem more likely for a quote by Horwitz to be misattributed to the better known Horowitz than vice versa.
According to chesshistory.com, in October 1959, Al Horowitz wrote:


  It is axiomatic in chess that it is easier to achieve a winning game
  than to win it. One bad move nullifies 40 good ones, and precision
  technique is of the essence even when the game is well in hand.


The same can be found in his book, “All About Chess”, written in 1971.

However, in the Chess Review magazine (November 1961), Al Horowitz calls this quote an “adage”.  Given this, I think that Al Horowitz is not the author of the quote, but thanks to him we know about it.

As for Bernhard Horwitz, I have not found reliable sources indicating that he is the author of the quote. At least, it is strange to me that it is not mentioned in his books.