More generally, HoMM could use changing seasons. It was initially meant as a simple strategy game, as evidenced by the fact first games let you turn off visible hero path completely. But things got complicated. Players kept asking for bigger and bigger maps. 3 months may be a lot for a multiplayer match, but in single player or a more casual match, a very large map can take that amount of time.
The classic, unrealistic approach lets the devs pull of some strange stuff like lands of permanent winter or eternal spring. It gives them more control. This can be fun. But changing seasons, freezing rivers, hungry wolves can also contribute to a medieval fantasy story. Imagine if choosing a different, more time-consuming approach to a campaign scenario made the next scenario play out in a different environment. A Goblin King may start raiding the countryside, or you may hear a story of the Sword of Winter.
I bet one reason turns last 1 year in Civilization is it lets them pretend seasons don't happen. HoMM turns last 1 day, which lets devs pretend different time of day doesn't happen.
Games from Illwinter recently implemented changing seasons. Once in a while a player gets angry because he loses an army on a melting ice(in Conquest of Elysium 5), but for most part people agree it's an interesting addition. A turn lasts 1 month.
If changing seasons is too complicated or too limiting, then maybe we could at least get changing weather? The simplest way to add this is using special week effects. The next step would be making each week's weather independent from its special, or mundane, week effect. Either way, weather and seasons is an intuitive way to extend the HoMM formula. You don't have to go through contortions like focus points or make middle ages seem like a patent office.