It could be worse than that. Our past two opponents were Hussein's Iraq and the Taliban.
Iraq is a desert country with a highly centralized population along the Tigris/Euphrates river valley. This combines to give a swift moving distance engaging force with air dominance a huge advantage. Of course that Hussein was the clown prince of misunderestimation helped.
The Taliban were in a mountainous country with little technology, no artillery, no infrastructure, and a population who supports whoever seems to be winning.
North Korea militarily has dated but servicable equipment, mountainous terrain, 10,000 pieces of artillery, a navy, a air force, a special operations component. NBC warfare capability (questionable on th "N" though). A population that may or may not support their opressors.
Further North Korea could wipe out Seoul, South Korea with the 3,000 to 4,000 artillery pieces in range.
Our side (counting South Korea, Japanese, and USA as our side) could lose the amount mentioned in the first few hours of the war.
The question is what would be the war aims of North Korea?
Completely taking over South Korea would be beyond the North's capability by itself. Destroyning Seoul and negotiating an end to hostilities is much more likely.
But it would also depend on what our goals were.
Putting US boots on the ground throughout the country would be a nightmare. Perhaps there could be another plan?
I have no idea, but what if the entire military infrastructure were to be attacked, repeatedly, via aerial assets? Once the smoke settles, let South Korea have what remains in the same way that East Germany was returned to West Germany.
A few tough weeks, but perhaps better in the end? I am a novice at this; other opinions appreciated.
MOABS, daisy cutters, fuel-air bombs, F-18s, cruise missles, Tomahawks, Seasparrows, etc; those 3 - 4,000 artillery pieces wouldn't last one hour.