Money was tight at the Disney Studios in the early years. Even when Mickey Mouse was wildly successful, the company had to conserve cash. That explains who voiced Minnie Mouse in her early years...
It was Walt Disney himself! Minnie Mouse originally just squeaked and said a few words, so it was easy for Mr. Disney to save money and provide both Mickey and Minnie's voices.
As the company coffers grew, Mr. Disney was able to retire from voicing Minnie Mouse. The task was taken over by Marcelite Garner, who gave Ms. Mouse the voice and personality we all know and love.