There's a quote of Mozart's about Handel that got me wondering how familiar composers like him and Beethoven were with the latter's music? Was it performed at all in Vienna during their time? If not, was there ever a Handel renaissance, like in the case of Bach?
Handel was actually very well liked and quite widely performed during the classical period and never really fell out of fashion like Bach did. For instance, there were performances of Messiah from Florence to Mannheim in the 1770s. Indeed, Mozart made his own orchestration of the piece which better conformed to the musical taste of the time. Mozart said of him "Handel understands affect better than any of us. When he chooses, he strikes like a thunder bolt," and Beethoven simply called him "the master of us all". However, I think that in general people stopped producing his operas and they were left to gather dust till the twentieth century. That is not to say however, that composers would not have owned scores, enjoyed them and drawn on them for inspiration.
If you don't get a satisfying answer here you might consider posting this on /r/classicalmusic