There's lots to enjoy in this early technicolor short, which is, I believe, an original story which aims to be in the tradition of the existing classic fairy and folk stories on which many other Symphonies are based. However, as Eutychus point, this short is marred for a lot of people because the moral seems to say "don't try to expand your horizons". I don't believe that is the intended message, since that goes against Walt's own achievements. I think the message is supposed to be "Be Yourself", but it's all muddled up by a somewhat confused story.
When the mouse dreams of flying he imagines he has bird wings, but his reward for saving the fairy is a pair of bat wings so he never really gets a go at flying as he imagined it. At the end, when the fairy says "Start anew, Try your best, Be yourself" it doesn't quite ring true, because he was trying his best even before he had the bat wings – he'd inventively tried to make wings for himself and he'd shown bravery, kindness and politeness. I suppose the cartoon tries to say that all his positive traits are enough for him to go far in life, without him wishing to be something he's not, but the trouble is he never wished to be something he wasn't – he wanted to be himself with the added ability of flight.