Do you complete the adventures/quests/whatever in Heart of Winter (and Trials of the Luremaster) after you've finished the main game? Or do you need to take a break from the main quest in order to do them, like with the Tales of the Sword Coast stuff in Baldur's Gate?

Both options are possible.
You can finish the original game and export your characters into a HoW game and into a new TotL game afterwards (just restart HoW for this and begin immediately).
Or you could finish the expansions within the normal game.

Be aware that the rest of the main game can get very easy with all the XP and equipment you can get in the expansions.

I think the player is supposed to play Heart of Winter and Trials of the Luremaster before finishing the main game.

You can play Trials of the Luremaster within the Heart of Winter expansion and are returned to the Heart of Winter upon completing the Trials. After finishing the Heart of Winter the party is returned to the main program and then you have reached a dead end if you imported your characters because you no longer have those items that opened the stairs to Poquelin (or whatever his name was).

So my advice would be: Open those stairs, return to Kuldahar, do the Heart of Winter and Trials of the Luremaster and then return to those stairs and say "Hi" to Poquelin and finish the main game.

Thanks.

Most IWD players had finished IWD before HoW was released and exported their characters to continue with the expansion, so it's the classic way.

There's an item you can get when you can't return to Kuldahar any more to start HoW from within the game, if you export your characters after finishing the game it can be upgraded in HoW. Be aware than container content can't be exported.