No the skis have independent mounts, but the wheels will retract up and down normally for the sea ice runway or regular strip..(top foto)
The nose ski will not take a lot of stress as it has very small mounts.. They bring the port and starboard skis in contact with the ice /snow and let friction slow the aircraft and then bring the nose down O-so-gently and then pitch props.. We used to get really pissed, as new in training Herc jocks would drop the nose to hard on the ice runway and the nose wheel would cut a trough in the ice.. Then equipment ops would have to haul water to fill and replane/surface the runway.. The herc heros would have to explain a broken front strut or worse. In 1980 if I remember right, a complete ski package was about a million bucks.. Flying down to McM from Christ N.Z. is normally about eleven hours dragging skis as they do not retract fully so top end is in the neighborhood of about 135mph and flying a point of no return both ways.. You go down, your toast..
Herc on sea ice:

Open field landing on a glacier:

C-5 (Wheels) on annual sea ice McMurdo Sound:
