I have a relatively cheap filter on the kitchen sink cold water tap, and I use ice in a large thermos style water bottle, but I too prefer cold/chilled to room temp. I can drink room temp fine, but I like it cold more.

I get it out of my fridge’s dispenser. Sometimes I put ice in there if it’s a hot evening. The flask cost me $10 which is cheaper than a Camelbak. Lasts me a few days between refills. Honestly a good life hack if you’re used to have a glass of water by your bedside.