Green_Hilltop: What, I've played the game for years and never knew this! I always thought the hero's speed was based on the terrain and their pathfinding skill. Is there somewhere a handy FAQ that lists things like these? I think I read the manual and it wasn't there (or I might be mistaken and only read other HOMAM's manuals). Does this work in the later games as well, by the way?
I think of it like this:
-Slowest creature provides base number of move points for the hero for the turn. Feel free to have a nearby hero hold all the slow creatures overnight.
-Logistics provides a multiplier. Stables (HoMM3) provides another bonus.
-Oasis, Rally Flag, etc. provide some extra move points.
-Moving over rough terrain costs extra move points per tile. Some terrains cost more than others (Snow and Swamp both being pretty bad, while rough terrain is worse than grass but not as bad as snow). Roads cost less move per tile than grasslands; cobblestone road allows faster movement than dirt road.
-Pathfinding reduces/negates the move penalty for rough terrain.
-At least in HoMM3, moving on a diagonal costs slightly more than moving straight horizontal/vertical. I think this also applies to picking up resources; if you are walking past a pile of gold, then grab it when it is orthogonal, not diagonal.
At least in HoMM3, if your army is moving over their home terrain (or was it if you have at least one stack for that terrain, or was it if the majority of your army calls it home terrain? I don't remember), then you don't suffer the move penalty for that terrain. So a hero leading Tower troops has no problem moving over Snow.
I forget which details apply to which games. I remember one of them actually displays larger/longer arrows for the path when the tile costs extra movement. This might have been HoMM4?
Green_Hilltop: Thanks for the awesome tip! I usually don't scout and have just few heroes that are the power team, securing the area, but I play only singleplayer where it usually works.
Scouts are great for uncovering map so that your primary hero knows where to go and not to waste time going. I prefer to stack everything strong on a single hero to kill things with fewer losses, and to be able to tackle stronger enemies.
ZFR: That's why in HoMM2/3, it's extremely useful for scouts and supply runners to have 1 of the fastest unit, instead of the weakest one (though I usually don't waste level 5-7 units on them). Like the serpent fly, or griffin. And powerful heroes on mop up missions might find it useful to have just one stack of the level 7 creatures (which usually have extremely high speed). It's also why when you can't afford all units, always leave out the slowest ones. And even if you can, it might be useful to leave the slowest ones for castle defense in order to get more speed.
^Pretty much this, though off-hand I can't think of a Level 4 that I'd place on a scout. If they are worth buying, then they are worth buying for the combat hero.
ZFR: Cavaliers are upgraded to Champions for free at Stables located on the Adventure Map.
Oh snap! I didn't know this! I guess it never came up because any time I had unupgraded Cavaliers, I got them from a Castle town, so I already had the Stable move bonus.