Ttyjukl

I always make tea with boiling water - not water that is almost boiling, not water that has boiled and stopped boiling a few seconds earlier - in my opinion, for the best tea flavour the water must be boiling as it comes out of the kettle into the pot (or cup).

My wife is not so obsessive, and will often leave the kettle to switch itself off, then, after as long as a minute, pour the water onto the tea (she does admit that tea made by me is far superior to the tea she makes).
Anyway, I've found that tea made by be (boiling water) cools to a drinkable temperature faster than tea made by her (boiled, then very slightly cooled water). But that seems scientifically impossible - or could it be explained in the same way that warm water freezes (when put in a domestic freezer) quicker than cold water? Just clutching at physics straws here!

Maybe the whole thing is my imagination.

There is a good chance that your tea is cooling faster.

This is somewhat counter-intuitive, but it's because the only variable here isn't the temperature.

Evaporation is also very important in the cooling of the tea. The kettle probably has much less available area to release the steam, so the air above is saturated. This will lead to a much slower rate of evaporation, compared to when the boiling water is exposed to open dry air.

The rate of evaporation depends on the surface area and vapour saturation in the air. A kettle has a small opening to exchange it's saturated air with the surroundings, while the open cup can easily move away the saturated air through natural convective currents and new fresh air can come in to take it's place.

If you put some sort of loose covering on your cup that emulated a kettle (be careful to make sure steam can still get out, just not as easily) you should see it remain quite a bit warmer.

Does tea made with boiling water cool faster than tea made with boiled (but still hot) water?

In short, yes. The rate of cooling (temperature drop) will be higher when the liquid is boiling than when it has already reached a temperature closer to ambient temperature. However, as it cools, its rate of cooling will slow down, and it will reach the ambient temperature of the room more slowly than another cup in the same environment with a starting temperature closer to ambient.

I've found that tea made by be (boiling water) cools to a drinkable temperature faster than tea made by her (boiled, then very slightly cooled water)

Your classification for drinkability probably includes how well steeped the tea is and how much of the detectable compounds have transferred into the water. That process happens faster with the hotter starting temperature. There may also be some psychological bias in wanting to be right.

could it be explained in the same way that warm water freezes (when put in a domestic freezer) quicker than cold water?

The notion about warm water freezing more quickly than cold water is probably because water passing through the hot water heater has picked up more minerals/sediment/seeds for crystallization than water which has not.

Think about it this way: You bring a pot of water to a boil. Once it's well boiling, you pour equal amounts into identical mugs, one with tea and the other without. You start the timer for tea made your style. You let the other cool down for a minute, then add tea to the second and start the timer for tea made your wife's way. You stop the timers when the cups reach the temperature you classify as "drinkable." You are going to stop both of those timers at pretty much the same time, but the timer for tea made your way is going to display more time on it, because you started the other one after the cooling process was already underway.

Note: If you leave the second cup in a closed, insulated tea kettle not exposed to open air above, and put the first cup in a poorly insulated mug with an open top where steam and heat can easily leave, that first cup might indeed reach "drinkable" temperature more quickly than the second.