Here's a see through side-view of a toilet bowl. As you can see there is an INTERNAL TRAPWAY
to the toilet bowl. This suggests that you will need to continue working on thawing the toilet bowl out
... not the drain pipes.
If you have a tub and/or sink near this toilet then you can be sure that the ptrap
(see picture) to both fixtures is also frozen and they will not drain, but the main drain pipes and branch lines should be OK as long as they are pitched corretly.
You could try to thaw the toilet using, of all things, an electric blanket
wrapped around the toilet for a longgg time, or you could actually SUPER HEAT the bathroom using a PROPANE type salamander
(can rent these... see pic.), but first, try a warm water technique where you pour warmed water into bowl and then suck it out with a wet/dry vac. after it cools.
... that may help here. Finally
, if you don't have these things then you will probably be best to remove the toilet from the flange, take it outside and use warm water on both the bottom and the top to unfreeze this baby.
See how you make out with this... then we can talk about winterizing your cabin so this won't happen in the future...
Let me know what you think on this... ***STATICFX..I was posting as you were....good advice there...***