I think Quichote's horse symbolizes a link between the past and the future. Rossinante is a combination of two words: "rossin" - a nag, and "ante" meaning "in front of". By giving this name to his low-rate horse, Quichote expected it to surpass all the others and become the best stallion in the future. As every horse should match its master, Quichote expected his own future to be bright and glorious too.
I am not sure, though.