Well, an old cartoon race horse often has a slower gait and might show signs of wear and tear on its body. Its eyes could reflect wisdom from all the races it's been in. Also, the design of its saddle and equipment might look outdated compared to modern ones.
The cartoon boy could be sick and funny because of a crazy virus that makes him act strangely and amusingly. Or it's just the creator's way of adding humor to his illness situation.