I won’t speak for the PNW, but I know New England has a warehouse where they store fields during the offseason. During the season, they use PODS storage units to transport the field (one field fits in four PODS) between events. Also note that New England uses a full set of road cases and ships all the carpet to be used in a season in the PODS, which not every district does, and this increases the shipping requirements.
The PODS usually get dropped off at the venue school a few days before the event and sit in the parking lot until they get unpacked and set up. After the field gets torn down, the PODS get loaded, and the company takes them to the next venue.