As Armor says that bearer cannot take more than 1 wound, only one wound can be assigned to the bearer. If the bearer of armor also wears The Ring, only one burden is added instead of that wound.
However, if the text of Armor said "prevent wounds" instead of "cannot take wounds" the ring-bearer wearing the ring would have to take 4 burdens (if the minion is damage +3).
There is an example of Isildur, BoH wearing the Ring and about to take a wound (burden) which was to be prevented by discarding The Sapling of the White Tree, except that it cannot be done because it prevents wounds, not burdens.
That example is made in Comprehensive Rules 4.0 under response.
I disagree with part of this statement. Wounds happen one at a time. Because of this,
Armor essentially says that wounds can not be assigned to the bearer *if he has already taken a wound in this skirmish*. Therefore, your first example is incorrect. If the RBer is wearing the one ring, he will still take burdens, as he has yet to take his wound for the skirmish.
Another example:
Gondor man with
Armor loses to damege +1 minion. If you use
Sapling of the White tree to prevent a wound, this man would still take the second wound, since he had not yet taken a wound during that skirmish.
Your second example is also off if Armors text was manditory prevention (as I assume you mean). There would be 2 manditory triggers (preventing the wounds, and the replacement of wounds with burdens) In tihis case, if the ring were put on after the RBer had taken a wound for the skirmish,
Armor would could prevent the other wounds before they were converted to burdens via the ring because the FP can order the manditory triggers.
The sapling example is correct because Sapling is not manditory. Since all manditory triggers happen first, the wounds are replaced with burdens before the FP can use Sapling. In other words, the RBer is no longer taking a wound when the FP can respond with Sapling.