It depends on my mood. If I want a drink that is refreshing on a hot day then I like te water really cold and will sometimes add heaps of ice. If it is just to quench thirst I'm more likely to get it from the tap. My husband has a water filter he keeps in the fridge so if you asked him it would always be filtered from the fridge.
I'm definitely straight from the tap kind of girl. I'm not a huge fan of drinking natural water and really will only do so to quench my thirst opposed to drinking it to ensure 2 litres of water per day.
I find chilled water has a slightly different taste (it's as though you can almost taste the chemicals in the water) even if it's filtered. It could just be my taste buds or the water in Sydney but having grown up in Adelaide where the water was absolutely horrid, I may have taken my dislike of water into adulthood simply because of bad experience.