It's because of the steam in the water. If you pour hot water into a pot, you'll see Steam rise out of it but sometimes it gathers with the rest of the water
it simply hasn't evaporated but it's about to
Steam is actually tiny droplets of water in the air (actual vaporized water is invisible). I guess tiny droplets of water into liquid water would not change anything :) I think hot water dissolves a lot of sediments while running through the pipes and tap, while cold water dissolves less stuff. Not all taps/pipes have this effect, and if you take cold water from your tap and boil it, it will still be transparent.
Everybody knows hot tap water activates and releases chlorine and other elements that clouds water, in cold water these elements are not evaporated but they are still there
it simply hasn't evaporated but it's about to