In this episode, Zack & Cody try to save Tippy the horse from being sold. The sneezing comes from the scenes when Tippy is allergic to the hair of the hotel's engineer, Arwin.
Tippy's sneezes are at 7:01, 7:03, 7:05, and 7:24.
http://www.dailymotion.com/video/x317e5m