I think that Alty only played Horwich RMI on three occasions:
(1) 20th October 1973
Altrincham 4 Horwich RMI 0
FA Cup Third Qualifying Round
Goalscorers: Lennie Dickinson; John Owens; the mighty Joe Pritchard and someone by the name of Graham Heathcote.
I remember watching this match from the Popular Side - one of my earliest experiences of Alty in the FA Cup.
(2) 1st December 1987
Altrincham 1 Horwich RMI 2
GMAC Cup Third Round
Goalscorer: John Timmons.
I believe that the Horwich team included former Alty striker, Micky Moore, and a promising youngster by the name of Phil Power (and they went on to win this trophy, defeating Weymouth in the final).
Horwich's manager was Les Rigby, who had a rather dismal spell as Alty's manager during the 1975/76 season.
Alty's manager, inbetween his after dinner speaking engagements and Piccadilly Radio duties, was a certain Tommy Docherty.
(3) 16th March 1991
Altrincham 5 Horwich RMI 0
FA Trophy 4th Round
Goalscorers: Nigel Shaw; Nicky Daws; John Brady; Mark Hughes; Paul Showler.
Marvellous days!