In the past, the FCC has found that antennas mounted on trailers to be considered as temporary construction. In order to license a facility, the tower must be of "durable construction", meaning it is attached to a durable, non-movable surface and connected to a permanent power source. Therefore, you are unable to license a tower that is mounted on a trailer.
The only time when a trailer mounted tower is acceptable is in the case of an already licensed station needing to temporarily move to a different location and only if the FCC has granted a Special Temporary Authority to use the temporary facilities.
Citations: Broadcast Towers, Inc., Order, 26 FCC Rcd. 7681, 7686 (MB 2011); see also Manitee Media Corporation, Letter, 33 FCC Rcd. 6685, 6690 (MB 2018).