Paul,This is not a hidden verse. The reason it does not appear on radio or Jean Ritchie's recordings is because it is clearly a thinly veiled drug reference.
The snow will not thaw = the cocaine is not dissolving in the ether.
And the stove will not draw = the bong is clogged.
There's ice in the water churn = someone put methamphetamine in the punch bowl.
In the mud and snow you're sloshing = you're taking too much brown heroin (Mexican Mud) and too much cocaine (see first line).
Trying to do your bit of washing = you're trying to clean up your habit, but obviously not too successfully (see previous line).
And the kindling will not burn = the marijuana is of poor quality.
Those of you who remember Spiro Agnew (former Baltimore County Executive here in Maryland) will know that we in Maryland are more keenly aware of the drug pushers' use of popular songs, especially folk songs, as a vehicle to vend their dangerous products (see PUFF, THE MAGIC DRAGON).
I applaud the BBC and Jean Ritchie's record company for standing up for the family and for all that is right in this world by not falling for the tricks of the notorious drug distributors.
Big RiB ;)