Eschalon developer Thomas Riegsecker talks about weather effects in Book II on the official Basilisk forums.
Weather has an effect, but not in the sense that you can freeze to death or drop dead from heat stroke in the middle of the desert.
In Book II, weather has an effect on your Move Silently skill (this skill is enhanced during bad weather because your natural sounds are covered by wind and rain). However, it also gets very dark at night during a storm and torches can blow out- try relighting a torch in the rain; you are better off using magick light. We are working to adjust some spells during rain and snow conditions (what happens to Fireballs in the rain? Deep Freeze in a blizzard?). Ranged attacks with arrows and thrown weapons will suffer a penalty during windy conditions.
Overall, weather is meant to enhance the visual and audible realism of the game world and maybe force the player to alter their play style when an impending storm is coming (better hold up for the night in the Inn and head out in the morning- no need to wander the dark woods in the rain).