So today I beat the level 7 of the last campaign The Sword of Frost in 3 game days. That's three days. Yup, three. For the penultimate level. Just grab the dragon from the city you start with, go south and Bob's your uncle.

I actually found the later levels of each campaign much easier than the first few. With the hero carryover you become so powerful and get all the good spells from the start, you can just mop the floor even with just the starting troops. Not that the first few levels were difficult either.

Aaaaaand the campaigns are finished.

Weird ending. Without giving any spoilers, could you at least tell me if the story continues later? In HoMM 4?

Chronologically within the game world HoMM IV is supposed to be happening after the last Chronicle.
At least the list I've pasted into my own play list. There are different fan made lists, though, and no clear consenus. But then I don't think the devs and publishers have, either.

Will the Sword of Frost story be continued?

Dunno. I haven't got that far yet, and my notes don't say.

Tarnum gets a little more story in HoMM 4, in the Might faction's campaign. He isn't the central character, but he is present. The story isn't really directly about the Sword of Frost (or AB), however. I gather that both of those swords were destroyed as part of the prelude to the world change for HoMM 4, per the intro for 4.

There is no particular order to play the HoMM 4 campaigns (for the base game, at least), so you can go straight into the Might campaign, if you wish.

I believe that the Death campaign in Heroes 4 Classic takes place after the Order campaign, but other than that, the campaigns do not refer to each other in any way and could be done in any chronological order.

That is true, Death does take place after Order, though they don't really intersect beyond a text reference.

Tarnum's story is finished in the Might campaign of HoMM4 in many ways

He dies near the end of the campaign, and goes before the ancestors who say he has redeemed himself for the crimes of his life by restoring community to the barbarian people and can now go to paradise.
But he asks to keep being the Immortal Hero instead and they are cool with that... Kinda weird

the reason for that is because he enjoys what he did helping the living while he was immortal and he wants to continue to do that (which he still does in homm4 campaign)

So much for "No spoilers!". :P

Just as well that ZFR already finished it.

Necro is one of the many HoMM 3 factions I like. In fact the Conflux is the only one I actively avoid.

I'm trying a new play style in this the last of the Heroes Chronicles; play with both a gimped hero (Scouting, Mysticism, Artillery, Sorcery and no Logistics, Pathfinding or Wisdom) and use Auto-Combat.
So I finished map 7 in ten game days. At first I though it was going to be difficult with a Hero with 4 Crystal Dragons appearing, but once I got a second Azure Dragon it was easy.

Yeah, I ended up blitzing most of the maps in HC, AB and SOD.
The maps tend to be rather formulaic, using the same themes in every map, like Dragon stacks blocking progress in Sword of Frost.

I love HoMM 3, but I found the Chronicles to be enjoyable and providing some challenge only if using the gimped hero + AC "strategy". Thank JVC the game came with a map editor!

Nice. I might try a gimped hero challenge some time too.

Try it. Only way to make the HCs fun. Last map of Warlords of the Wasteland actually made me sweat a bit, with no Logistics or magic skills, and no secondaries (I missed Dessa with Expert Earth, Town Portal and Logistics specialty).

Anyway, I'm now at map 2 of Conquest of the Underworld, and I had the same reaction as you did. Then I remembered there was some discussion about it on GOG.
Looking up the map in the editor (and fixing it) it looks like a simple mistake of assigning the purple player to the wrong team. I assume it's supposed to be two hostile teams of two players each against the human player.
And even if it was no mistake I don't think it will hurt the map to fix it to make it more challenging.

Warlords of the Wasteland and Sword of Frost were actually quite fun playing with handicaps, but this particular Chronicle is a disgrace, with its shoddy design (I had to edit the Teams in half of the maps!) and being laughably easy with free resources everywhere and all but the final enemy being low level. The only map with some clever design and a strong enemy was the last one. After neglecting to strengthening my army and just rushing for what I thought would be a piss easy fight, I actually lost the first time I fought it (using auto-combat) thanks to Dweezil Zappa having the Armour of the Damned and Tarnum having no magic skills.

But when reloaded and brought along the unrecruited troops from two castles, Dweezil countered the Angelic Alliance's Prayer spell with Mass Dispel, dispelling Slow, Curse, Misfortune and Weakness on my troops as well. :Facepalm