If you live in the part of America to which winter time brings cold temperatures, you are always delighted that when you turn on your tap water or shower water and give it a little time to warm up, that the water pours our fairly warm or even hot, but the credit for that temperature change goes primarily to your water heater and you definitely pay for that convenience. However, there are times when we need or desire cold water, but there isn't anything built within a typical house that impacts the temperature of the cold setting for the water, so that during the dead of winter, you will often find that cold tap water, really is ice cold water, especially when you first turn the tap on! Why is that?
The origin of the water that is tapped into our homes typically comes from lakes, streams, rivers, and whatnot that surround our particular community to which this water is piped and pumped underground, and once you get piping situated about 4 feet below the earth's surface that water stored there will find its equilibrium at around 50-55 degrees, so that even if the water entering the pipes is below 55 degrees or well above 55 degrees when it enters the piping, it will over time moderate its temperature to conform to the earth soil that surrounds it. However, not all piping is dug to a depth of 4 feet or lower and further the piping that is in close proximity to a particular home is typically closer to the surface of the land, meaning that it is more susceptible to surface air temperatures and additionally because water is stored often times in large water towers that water there too is susceptible to air temperature.
The bottom line is that the air temperature most definitely affects the temperature of the tap water that comes out of our faucet when we turn the dial to cold, so that in the dead of winter that water coming out of the tap will be appreciably colder than the hottest day of summer, with probably a temperature difference easily exceeding 10 degrees, even though the faucet dial is in the exact same position and further, these temperature extremes will be more noticeable when the faucet is first turned on.
If it wasn't for the underground piping in the first place and the fact that deep water lakes have remarkably consistent cool temperatures far beneath the surface, than cold water would be far more problematic in achieving our home water needs and desires. We shouldn't be surprised that the air temperature does affect the water temperature of our tap water, however, if it wasn't for the actuality that the water is primarily pumped to us deep underground to which the ground temperature is quite consistent and thereby provides the basis for our tap water being cool, we would not be able to have pretty much cold water on demand. That said, not too unexpectedly, when the temperatures drop or rises appreciably, our cold tap water pretty much follows suit.