Final answer:
Joseph Haydn most influenced Mozart's music during the Classical period. Haydn was a key figure in the development of classical music forms, and his work directly impacted the evolution of Mozart's style.
Step-by-step explanation:
The composer who most influenced Mozart's music was Joseph Haydn. This is reflected in their enduring friendship and mutual respect. Both composers were prolific during the Classical period, and Haydn's contribution to the classical forms—particularly the symphony and string quartet—was immense. Mozart admired Haydn's work, and the influence is noticeable in the evolution of his own musical style.
It's important to note that while other composers like Beethoven, Brahms, Schubert, and Chopin were also significant, they were part of the Romantic era, which came after the Classical period. These Romantic composers did look back to the great Classical composers for inspiration, including Mozart, but Haydn directly influenced Mozart during his lifetime, making him the most relevant answer to the question.