There's no ice, and besides, it's too cold for iced tea today.

Literal

Ice [subject-が] not-exist, moreover today [topic-は] iced-tea [object-を] drinking [for-には] too-cold.

その上 means 'moreover, on top of that.' 寒すぎる uses すぎる for 'too cold.' には marks the purpose ('for the purpose of drinking'). Two reasons stacked — no ice available AND it's too cold anyway.