HoMM3 HD is a mod (add-on) for the game Heroes of Might and Magic 3.

It's actually easier to save, calmly go for a smoke/make a phone call/have some tea/buy some beer, return, and continue playing.

Firstly, it's not easier – you have to save and then load, and before that, you still need to agree on it.
Secondly, both players lose time – the game stops during the break.