I have never learned to ski and am rather suspicious of them. Far too many images in my head of people returning from skiing holidays with broken limbs I suppose. I feel in control of snowshoes.
Cross country skiing and downhill are two very distinct events. CC skiing in deep snow and doing the same with snowshoes do not differ all that much. I have tried both, though much more with skis, and in level open country skis are better, in hilly areas and thick forest snow shoes tend to be easier.
Search "pulkka" or "ahkio" for old and tried solutions for moving a lot of things in snow. I admit that that your sliding plastic sheets pack better. I have seen in past a kind of origami ahkios that are made of sheet material.
In the last few years there has emerged a new type of ski "sliding snow shoe" that is a kind of cross between the two. I haven't tried them myself but people I know are fairly experienced trekkers say that they are not too bad.