What I'm interested in learning is whether windmilling causes a gyroscopic effect to resist movement or a paddling effect.
I'll take bite at that apple - Yes
, windmilling (done properly) does
affect our forward/aft rotation! It's just that other factors affect us a lot more.
Angular momentum must be conserved so when a body-part is rotated, something else must give - but the result is not necessarily 'equal' and not necessarily 'opposite' in our typical intuitive way of seeing things. Rotational results are tricky to pin down because the reaction is not always what you'd expect. Just hold the axle of a bicycle wheel, spin the wheel and try to "tip it" to the side. Dang thing will try and rotate 90-degrees from the direction you tried to tip it!
With this in mind, consider that once in the air, a skier can still change their orientation (position) by implementing independent body-part rotations. If anyone needs proof, carefully examine this video from the days of Skylab
Watching this video, note that a few of his gymnastics begin as directly-forward whole-body rolls then turn into whole-body spins and eventually end up as forward rolls again. He does several routines like this where new whole-body rotations in a different direction seem to come out of nowhere.
How? Look carefully at his overall orientation and especially at the axis of each rotation with respect to the orientation of that large 'wheel' he's performing in. Notice that when spinning his whole body has changed its axis from parallel to the wheel to being off by quite a few degrees? And when he comes back to a forward roll, his axis is back where it originally was?
We see the same idea when a cat falls from an upside-down state and it quickly rights itself before landing (given enough time). If we drop the cat from a North/South orientation we'll find it lands with something of an East/West orientation. This is a result of rotational transformations the cat makes to achieve flipping over - and staying flipped over until landing, even though it has stopped rotating anything.
Oh, and if you don't think this applies to skiing ...check out the first segment of this video
Once again this isn't a matter of 'balance' while in flight but rather a matter of orientation in relation to something else
. For jumping skiers it's a matter of orientation to the surface at the moment of landing. Most of the input for a successful landing comes at the moment of lift-off but controlling one's orientation to airflow is essential for longer jumps. Implementing rotational contortions can help correct launch-errors but may cause more harm than good if airflow is mucked up by such arm and leg motions.