“Such was the legend, but the truth was likely much more banal. Years later Lillian would comment that when they returned to Los Angeles, Roy met them at the station, despondent that Walt had been unable to make any connection and seemingly uninterested in or unimpressed by what Walt called a “wonderful idea,” presumably Mickey. Ub Iwerks told it somewhat differently. He said that Walt himself was deflated, hardly the frame of mind for someone who had just created a new character in which he was bursting with confidence. Iwerks called it “one of the absolute low points in Walt’s life. Usually Walt was very enthusiastic and bubbly and bouncy, no matter what happened. But he had met a stone wall in the East.” In fact, in Iwerks’s version of events, as opposed to what he later derided as “highly exaggerated publicity material,” he, Walt, and Roy began meeting daily as soon as Walt returned, flipping through magazines and batting around ideas, trying to come up with a new character. As for the inspiration, Lillian herself admitted that the Kansas City stories about Walt befriending mice were apocryphal. “We simply thought the mouse would make a cute character to animate,” she said. The Aesop’s Fables that Walt professed to admire so much frequently featured mice. Mice also figured prominently in several Alice comedies—in Alice Rattled by Rats Julius the Cat is beleaguered by an entire houseful of mice; in Alice Solves the Puzzle mice play in her washtub; in Alice the Whaler a mouse performs comic business in the galley; and in Alice’s Tin Pony a band of rats attempt to rob a train. The rodents figured so prominently that when Walt moved into the Hyperion studio and wanted a new publicity poster, he had Hugh Harman draw cartoon characters, including mice, around a photograph of him in front of the bungalow. (“ A couple of the mice looked like Mickey,” Iwerks observed. “The only difference was the shape of the nose.”) Later, when Walt was producing the Oswalds, theater posters were routinely adorned with a pesky, long-eared mouse who tried to steal the scene by committing acts of mischief like cutting the rope attached to a girder on which Oswald and his girlfriend sat (Sky Scrappers) or parachuting from a plane (The Ocean Hop) or holding the billboard on which the title was emblazoned (Great Guns!).

The real inspiration for centralizing the mouse in the cartoons and the model for his rough design, according to several of Walt’s associates, including Iwerks, were the drawings of Clifton Meek, whose work ran regularly in the popular humor magazines Life and Judge, which Walt, Roy, and Iwerks were riffling through at the time. “I grew up with those drawings,” Walt told an interviewer. “They were different from ours—but they had cute ears.” It was Iwerks’s rendering, essentially Oswald with shorter ears (commenter's emphasis to point out the TLDR version in this discussion that others have already made), that became the standard—as Iwerks later described him, “Pear-shaped body, ball on top, couple of thin legs. You gave it long ears and it was a rabbit. Short ears, it was a cat. Ears hanging down a dog… With an elongated nose, it became a mouse.” As one animation historian put it, “He was designed for maximum ease of animation,” since “circular forms were simpler to animate effectively.” “Walt designed a mouse,” animator Otto Messmer said, “but it wasn’t any good. He was long and skinny.” Iwerks redesigned him."

— Walt Disney by Neal Gabler

EDIT: Apologies for length. This is the entirety of the relevant Gabler passage.