The sky cells are highly uncomfortable and potentially deadly. Rather than freeze and starve, he hatched the plan to demand a trial by combat, as mentioned above. In the book:
"I thank you, my good lady, but I see no need to trouble Lord Robert," Tyrion said politely. "The gods know the truth of my innocence. I will have their verdict, not the judgment of men. I demand trial by combat."
But that was not the whole of his plan. He had a plan to win a trial by combat:
"And now I demand a champion, such as you have chosen for yourself. My brother Jaime will gladly take my part, I know."
"Your precious Kingslayer is hundreds of leagues from here," snapped Lysa Arryn.
"Send a bird for him. I will gladly await his arrival."
Jaime is one of the foremost swordsmen in the land, and known for it. He would have been an ideal champion, but Lysa wouldn't have it, which I'm actually not sure if she legally could deny his chosen champion:
"You will face Ser Vardis on the morrow."
"Singer," Tyrion said, turning to Marillion, "when you make a ballad of this, be certain you tell them how Lady Arryn denied the dwarf the right to a champion, and sent him forth lame and bruised and hobbling to face her finest knight."
"I deny you nothing!" Lysa Arryn said, her voice peeved and shrill with irritation. "Name your champion, Imp . . . if you think you can find a man to die for you."
"If it is all the same to you, I'd sooner find one to kill for me." Tyrion looked over the long hall. No one moved. For a long moment he wondered if it had all been a colossal blunder.
Then there was a stirring in the rear of the chamber. "I'll stand for the dwarf," Bronn called out.
He suspected Bronn might fight for him, and he knew how deadly he was on the way up, fighting through the mountain men.