As Grit dog mentioned, you can buy new water flush valves, $10-$15 is all they cost. Depending on model of toilet some are very easy to replace without removing the toilet, some will be easier to replace if toilet is removed but still can be replaced "in place".
Fix the water fill valve and most of your pile will go away.
The problem is just dumping a bowl of water will not disperse the solids, instead what happens is the solids drop and stay in place and the water from the bowl basically runs right off of the pile of solids..
Using the built in water valve allows water to rinse down the bowl and then that slowly drops over the solids softening them up so they disperse better instead of piling into a large lump..
Dig around and see if you can locate a model number on the toilet and then get the correct valve..
As far as freezing in cold weather, folks forget to either blow the water out of the toilet lines or forget to run some RV antifreeze into the bowl..