Unless you plan on using the trailer soon the 30 day warranty is kinda meaningless, especially considering where you live and the time of year. if the dealership is willing to do what's needed to make you happy I would take advantage of that and have them de-winterize the trailer and go thru a full PDI.
Is it possible for you to delay picking up the trailer until later (warmer) in the year and leave it at the dealer on their lot?? Then when it's warmer they can de-winterize, give you a PDI and you'll have 30 days to use it to see if there are any problems...just a thought.