I race both xc skis and on foot and in my opinion there two reasons xc skiers lay on the ground after a hard race:
- In XC skiing you lunge for the line with one boot maximally forward (first boot across the line wins). This is an extremely unstable position on snow at top speed in the final sprint to the line. Since xc skiing is unlike running but more like cycling in that the draft matters... there is most likely a group sprint to the line ending in a lunge where guys wipe out after they cross the line. It is easier to stay lying on the ground to catch your breath than it is to stand up after the finish(or hunch over hands on knees like runners do).
- A less significant reason is that some of your energy in xc skiing goes toward balance and staying upright. When you get really tired, the desire is to stop using the muscles that you have been stressing to keep you from falling on your ass. Laying down allows you to finally relax these muscles. There are literally dozens of small muscles in your feet, legs, core, and back that make micro adjustments to keep balance on skis. Because humans are engineered and trained daily from birth to stand on two feet effortlessly, most runners do not feel that standing or walking is difficult after a race (but some do put their hands on knees as they catch their breath for some relief).
Trust me. There is no drama going on here.