What is an "all-weather" aircraft? I've read a few times that such-and-such a plane is an "all-weather" aircraft, for example:


  The McDonnell Douglas F/A-18 Hornet is a twin-engine, supersonic, all-weather, carrier-capable, multirole combat jet.


This is quite intriguing and a rather odd thing to specify. 

A fighter that couldn't be operated in for example rain (perhaps because it might dissolve, rust or leak) wouldn't seem to be much of an asset to one's air force.

Similarly, I would not expect a supersonic fighter to be unable to deal with gusty winds, or a heatwave, or really, anything else the weather might be expected to throw at it.

What sort of jet would not be an "all-weather" aircraft?
“All-weather” is a little bit of a hold-over from the WWII days where severe weather was much more of a threat to the aircraft. Between less reliable engines, delicate and finicky instruments like artificial horizons, and limited anti-ice technology, flying in adverse conditions was much harder then. Becoming completely disoriented in low visibility was almost a death sentence.

Special planes were made with the sole purpose of fighting at night, and certain designs were better than others for all-weather operation.

Nowadays, world class military aircraft are all pretty much all-weather because of the 70 years of avionics, propulsion and airframe improvement.