Skiing vs running form.
Body and thus leg extension is more horizontal in skiing than in running, because there is no need to lift the body off of the ground to leap to the recovered leg – that leg is slid along the ground. I think the muscular actions of leg recovery are very similar, though – the more steeply inclined trunk recovers a lower leg, plus the weight of the boot, binding and ski help to make gliding the ski forwards a fairly natural leg recovery. It is important to state that leg extension is complete when the leg is in line with the trunk. Any hip extension beyond that is hyper-extension and is counterproductive in jumping, running, and skiing, as the full-body extension of these actions is increasing the distance between the head and the toes. Hyperextension will decrease that distance.
In cross-country skiing, the speed of your recovered foot before returning to underneath your body is not dictated by ground speed, as the ski is gliding over the snow. This means that the phase of weight transfer to the forefoot is longer, and one can take the time to sense the toes spread and their flexors activate.
The foot recovers toe first in skiing mainly because the toe is attached to the ski which remains on the ground. This makes the addition of heel-lift in cross-country ski boots particularly cumbersome. But it would be hard to eliminate, as the boots need to have enough depth at the heels for a deep groove to sit the boot solidly on top of a ridge on the binding to restrain lateral movement. One could eliminate heel lift by making the entire sole the same depth, but this would lift the toe pivot further from the ski – not such a great thing for control.
Because the arms are much more active in cross-country skiing than in running, there is considerably more spinal torque. Also, there is more counter-rotation of shoulders against hips in skiing and perhaps more pelvic tilt as well. The spine that is already extending in the forward movement of running and skiing is more powerfully extended against the arm extension of poling. This if often mistakenly described as “compression”, but the natural action of spinal opposition to arm extension in skiing can be compared to that in freestyle swimming – one keeps the spine long so that arm extension keeps the trunk moving forward and not caterpillaring along, as some recommend in skiing.
Here is a photo of Norwegian Bente Skari beautifully extending her body from head to toe, and poling without compression: