The two potential tax breaks that you could receive for such a situation are the following.
First, if you operate a business, or are self-employed, then if the travel trailer is a necessary part of your work activities, it could be capitalized and depreciated as a necessary business expense (think here of something like a travel trailer used as job site shack for a long-term construction project).
Second, if you took out a loan for this trailer, you might be able to claim a mortgage interest deduction. This is discussed in much more detail on another TurboTax question thread here: (note that if cannot see the full page, click the "see entire answer" button to expand it).
Thanks for asking this question, and good luck to you.