I also suspect you have a clog rather than a freezing problem.
However, I will say that I think a lot of folks spend way to much effort trying to "clean" their black tanks. My RV is going on 30 years old, we have had it for 10, and I never "clean" the black tank.
The trick to the black tank is
1) Use an enzyme treatment every time you use it (have to add more after every dump) and
2) Always dump when the tank is full. If it's not full, I use a little block of wood to hold the toilet flapper open and let the black tank fill up with water before a dump. This way you have a large volume of liquid to carry away any solid waste in the tank.
Also, even if you have full hookups, make sure you leave your black tank valve
closed all the time until it is full and you need to dump. In other words, you have to dump it manually when it gets full even though you are hooked up to sewer. If you leave the black valve open then all the liquids will flow out of the tank but you will build a "poop pyramid" on the floor of the tank that will not flush out properly.
If your tank is already gunked up than a hose-out may be in order, but for sure use enzyme in your tank and let those little critters eat all the gunk out of the system.
Steve
1990 Winnebago Warrior. "She may not look like much but she's got it where it counts!"