Secondary skills in Heroes 3.

It all depends on the choice of faction.

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And it may also depend on the size of the map.
For example, on a simple S-sized map, you might not need Wisdom because in a fast-paced game, you might not have time to acquire high-level spells.
And if you're playing on an S-sized map with a Stronghold or Fortress, then Wisdom is generally not needed :-)
But if the map is large, then IMO, Wisdom is the most important secondary skill.

And in general (I think I've already written this), for L and XL maps, the clear priority is Wisdom, Earth, and Logistics; if you don't develop at least some of these, I feel like a failure :-) Air, Tactics, and Intelligence are secondary in priority.
The remaining skills depend on the faction.
If you have many ranged units, develop Archery.
Playing as a Castle, develop Water and Leadership.
Inferno - Fire.
Fortress - Defense + Ballistics.
Stronghold - Attack + Ballistics.

Literacy, Estates - only for secondary heroes.
Scouting, Eagle Eye, Mysticism, First Aid, Luck, Learning, Magic - forget about them.
Depending on the scenario, Pathfinding, Navigation, Resistance, and Diplomacy can be very useful.

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With relatively small armies, a mage has it easier. However, with large armies, magic is no longer as effective - mages don't fare so well.

Well, I wouldn't say that.
A powerful mage with a large mana reserve and knowledge of most spells will defeat a strong warrior with a good army if the warrior is completely clueless about magic.

If the warrior doesn't crush the mage in 1-2 turns, he has a good chance of getting a severe beating :-)
But if the warrior has experience in Tactics + experience in Air with Haste, then...
Magic won't save him then :)