Unlikely in a 13 year old trailer, unless it has been grossly neglected. In a 30 or 40 year old unit, it would be more likely. It's all about maintenance.
The fact that the wood is exposed underneath is not the issue.
Scamp coats the underside with
fiberglass resin. Almost all floor rot comes from above: neglected
leaks from
windows, vents, plumbing, and, to a much lesser extent, rivets.
But it always makes sense to check. Pay special attention around the outer edges under
windows and inside cabinets. If there is a shower, feel for softness, and inspect underneath.