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Uphill has the right of way. This holds true for mountain biking as well.

Ascending has right of way, but use good judgement on if they are struggling and need a second. I usually let the other person go anyways and use it as an excuse to catch my breath. Haha

Going up always has right of way

I tend to agree but sometimes it just comes down to who has access to a spot to step off the trail or who wants/needs a break or who understands the etiquette or who isn’t so focused on something else that they notice so with me, either is ok.

When traversing mountain passes in a 4x4 uphill usually has right of way, but common sense and reason will sometimes dictate that yielding to the downhill is right and proper.

So instead of thinking of who has the right of way, why don't you and others think of it as a 4way stop sign and proceed as such

And skiing (skinning up).

In general I think of it as the person who's exerting the most effort has the right of way.

Yup. Unless they are on horseback, in which case everyone is expected to cease all motor functions until they have passed.

Going up has the right of way. https://www.rei.com/blog/hike/trail-etiquette-who-has-the-right-of-way

However, if you are descending and you are a large group, the leave no trace principles would dictate that the larger group would have the right of way because them stepping of the trail would have a bigger impact.

I'll be honest, every time I see someone on horseback I just gawk anyway so that's easy for me.

Saw some guy riding a horse down the sidewalk in Kittery at night a few months ago and I almost ran a stop sign staring at it.