1) If you have clans that are trying to move in winter they should go ahead and move if their supply is yellow. Only if supply is critical (red) do they need to encamp.
2) Clans that have other tasks underway (foraging or identifying etc) by default would be in a mode where they automatically do their task if they can and only if necessary will automatically encamp.
3) Also, you can't apply the two points to a clan that is "in training", so for example you can't train an explorer (2 turns) and study discovery (1 turn) and on the next turn apply the two points to your explorer still being trained. Ideally, you also don't want to apply the two points to a clan that has no discipline set at all either, because then after you subsequently train it in a profession you would have only two points in the discipline (apply 2 points discovery to clan, then train as explorer->explorer with 2 points in discovery). The (annoying) way to do it is to research discovery on the same turn you train discovery, then on the next turn apply the two points to the clan (making it 3) and train it as an explorer (1 turn).

Thanks great info!

Another random tip:

You can change research in the middle of a project and it maintains progress while you switch to something more urgent.

For example:
You started researching loremaster (3 turns) last turn. This turn it has 2 turns left to go.
You change research to agriculture (1 turn).
Next turn when agriculture finishes researching, you resume researching loremaster, which has 2 turns to finish.

Don't forget you are nomadic! Any time you do not need to train a clan, you can take 5 gold... or you can pack up your settlement, allowing you to move on the next turn. And as long as you settle again with one movement point remaining on the next turn, you are back in business, able to train clans.

This can be incredibly powerful, because your existing structures remain in place, functioning as always, gathering resources as always. And your settled clans continue to provide their contributions during the move. And by moving you can grab new resource opportunities, or just move in the direction of them.