You didn't give us much background to go on. You are from Home. I don't know what the weather extremes are there. What kind of trailer do you have? Is the underbelly enclosed? How big is your black tank? That type of information is helpful.
My advice - find some place warm to park it. You can buy 12 volt tank heaters that stick to the bottom of the tanks. I had them on my first trailer. rarely used them, but they worked when I did. They aren't going to help with the exposed plumbing, though. Maybe adding some antifreeze to the mix will help a little. Skirting the bottom edge of the trailer and putting a space heater in there may also help.
One thing guaranteed to open up the dump pipe, is to get your face right up to it and look in it. The longer you look, the greater the chances of getting a poop facial will be and the problem will be solved. Good luck. Let us know how it comes out (pun intended).
