The KC-390 has had a testing programme on unprepared field capability and the C-2 has had a testing programme on ice surface capability.
The thing about the C-2 was that there are questions relating to the undercarriage setup with respect to rough field because when the project was conceived 20 years ago it was to meet Japanese requirements at the time, which were based around the nations pure self defence posture. The notion of having an expeditionary air mobility capability that would fly to unprepared airstrips in the south pacific was well off the radar. Thus the C-2's under-carriage set up was design to meet the need of Japanese engineered permanent runways.
All offshore Japanese islands both large and small dotted around the archipelago had prepared permanent runways, the shortest was 900m so STOL was a requirement and Hokkaido through the winter frequently has iced runway conditions, thus the ice requirement.
However right throughout the nation there are very few unprepared airstrips like grass, dirt, packed coral or cinder rough runways. Frankly such things are not very Japanese. The very few grass runways that exist are for private light general aviation. This is a land with a love of concrete (Concrete production in Japan totalled 91 million tons in 1994 compared with 78 million tons in the United States) and if there is a need for a runway somewhere they do it properly, with mega tonnes of the hard grey stuff, not some half-arsed 3rd world strip of gravel.