(Updated)
It must depend on the triggering mechanism used by the mine and on the characteristics of the specific vehicle.
Land vs Water
The DMZ between north and south Korea is land, not water so I will address land-based mines.
I believe most military hovercraft are designed for use over littoral water. I can find no evidence that armies (as opposed to navies) make use of hovercraft to transport soldiers across minefields. There may be other factors which influence this choice but the outcome may be that no one has seriously studied the use of hovercraft for this purpose (though one or two more civilian organisations have studied the feasibility of using small hovercraft for detection of anti-personnel mines - and they don't address the triggering issues)
Mine trigger/fuze methods
TM-83 mine
If we take as an example the Russian TM-83 mine this has a two-stage trigger, a seismic sensor arms an infra-red sensor that finally triggers the mine. The mine can be set-back up to 5m from the road it is targeting.
Seismic trigger
A hovercraft travelling over ground supports it's weight on a cushion of air, that means it still exerts the force of it's full weight on the ground but spread out over a larger area than a typical wheeled vehicle. Because of that weight and it's movement over the surface it will still produce sound and some vibrations that can be transmitted through the ground.
A hovercraft produces more noise and vibration than many land vehicles (Ref, Ref) as anyone who has travelled in one or stood near one can attest.
It is hard to find relevant studies of hovercraft noise, one that sheds a little light on the subject is Hovercraft Underwater Noise
Measurements in Alaska which shows that hovercraft travelling over a frozen river produce more underwater noise than snowmobiles.
As an example, a single event (pass-by) hovercraft sound exposure
(LE) of 134.1 dB measured at a distance of 78 feet is approximately equal to 14
snowmobile events at the same distance.
Although both snowmobiles and tanks (the targets of anti-tank mines) are both tracked vehicles, in other respects they are not comparable. It is therefore difficult to apply this information to the subject at hand. At the least, this study does show that hovercraft can transmit significant vibrations through the surface on which they travel.
Infra-red trigger
A hovercraft also has engines that produce heat and therefore can be detected using an infra-red detector.
Type 72 mine
The Chinese Type 72 mine is triggered by a pressure of 300 Kg but is resistant to overpressure produced by anti-mine ordnance.
Pressure trigger
The skirt of a hovercraft might exert a force equivalent to less 100 Kg over the area of a mine. (Ref: "250 lbs/sf". Ref: "245 kg/m²", "202 kg/m²")
M75 Mine
The South Koreans are known to have deployed the M75 anti-tank mine. This has a magnetic trigger.
Magnetic trigger
A magnetic trigger would presumably be set off by any sufficiently large vehicle with a significant amount of steel in it's structure and with typical engine construction.
In "World Naval Weapon Systems, 5 Ed. By Professor Norman Friedman, PH.D." he says "Seemine anti-invasion … Fuzing is presumably magnetic to destroy landing craft including hovercraft" Which suggests he believes magnetic triggers in mines can, in principle, detect hovercraft.
TM-57
The Russian TM-57 anti-tank mine can be triggered by a tilt-rod fuze.
Tilt-rod trigger
Since the skirt of a hovercraft is usually in contact with the ground, it is possible that it could deflect a tilt-rod by the 25 to 30 degrees needed to trigger the mine.
BLU-92
The BLU-92 is related to the M-75 and can be triggerred by trip-wire.
Each side of the BLU 92 (an anti-personnel mine) has four hair thin trip wires that shoot out as soon as it lands. Ref
Tripwire trigger
The air cushion of a hovercraft, and its skirts, disturb the surface over which it is travelling for at least the whole width of the vehicle (unlike a wheeled or tracked vehicle)
It may be plausible that there is a possibility that the skirt, or debris disturbed by the air cushion, will strike a trip-wire with sufficient force to activate a mine.
Conclusion
I don't think there is sufficient evidence to settle this question either way. It must be possible to construct mines that are effective against hovercraft and it must also be feasible to design hovercraft to avoid triggering certain types of mine, particularly pressure-sensitive mines. However, many mines incorporate triggering mechanisms which are not defeated by the low-ground pressure characteristics of a hovercraft and which may present hovercraft designers with substantial difficulty.
On a personal note: if I had a hovercraft, the last place on earth I'd use it would be to make an incursion into North Korea.
