Strange that it would overheat unless there was a problem with either the cooling system or the design of the engine/cooling system is less than it should be.
Even at max power output, the cooling system should be able to keep up unless the airflow through the rad was blocked.
I'm not saying it's impossible, just that I'm surprised. Even for the temp to get up into the red zone (on more than one tractor, apparently) tells me that there's some marginal engineering involved.
Probably the best advice to give your wife in future, is that if the temp gets up into the red, turn the mower off and let the engine idle at about 1500 rpm with no load on it until it cools down to a normal level. Then either resume mowing at a lower ground speed/reduced load or shut it down. Keeping the coolant circulating past the rad (and fan) helps keep the hot engine block from boiling the coolant off until things cool down a bit, which sounds like what happened.
Be thankful it's not turbocharged, if it was I can almost guarantee you it would be a failure of the turbo from heat stress and cooked oil. Possibly not right away, but in the future.
Even with a non-turbo engine, it's a good practice to check the engine temp before shutting down. If it's higher than normal, let the engine idle for a few minutes until it cools off to a normal level. Repeated hot shutdowns shorten engine life substantially.
As it is you
MAY have a warped head/block from the coolant boiling out, if it didn't run until it cooled off your cylinders should be ok.
I've heard of rings losing tension in cases of severe overheating, more so with air-cooled engines though.
Be sure she adds some kind of coolant before she runs it any more, even fresh water will be ok to get it back to the barn. The proper coolant mix is a must before it gets loaded again, plain water doesn't do so well as the right mix of antifreeze and water, even in summer.
Like some of the guys said, you should know soon enough once you start working it again. If it starts using oil or losing coolant, you have internal damage. Keep a close eye on the oil and coolant levels and condition for the first while (next 20 hours probably). If the oil starts getting milky looking, you have coolant leaking into the oil side, if the coolant gets muddy, it's oil going into the water. Either is bad news.
She probably feels pretty bad about it, mine would be in hiding I think. I love her dearly, but the tractor is right up there in my affections too..
Good luck !
Sean