I think myself and theav8tr are thinking along the same lines. When it's a long flight, boredom in the cockpit and one overriding thing is there to focus the mind, in this instance the oncoming weather, all the mental ideas you have go into solving that problem.
I think the initial loss of A/P and A/T weren't the problem but a mental desire to get out of the icing layer/weather and certainly to not descend and enter even worse bad weather. Hence the initial response to climb and I believe initial pull-up actions.
Any later pilot responses to a stall warning that may have followed is another matter but I think that is one possible explanation of the primary actions taken by the crew i.e. nose -up input, and is being mistaken here as an incorrect response to the stall.