My (leftover) food in the fridge dries out quickly, and comes out in a pretty bad shape by the next mealtime. The weather here is pretty cold, hovering between 0-5 centigrade. Is it better to just leave my food on the windowsill (covered ofcourse), in terms of avoiding dehydration?
No the best option here is to cover food better in the fridge. Invest in some storage jars, or tubs, or better plastic wrap. If the food is in an air tight container it shouldn't dry out.
If you leave food outside you'll find you attract rats, mice and other vermin which will be very hard to get rid of.
What are the leftovers you are trying to save and how do you reheat them?
While the weather may be cold, I assume you are not leaving it outside?
I'd still leave it in the fridge but perhaps change how you are storing/reheating it.