From The Heroes of Might and Magic III wiki

Heroes moving over certain terrains get penalties to their Movement. Roads negate all such penalties, as does only having units that have the current terrain as their Native Terrain. Movement is compared to what it would have been on Grass. Magical Terrain does not affect terrain penalties.

Terrain type	Cost
Dirt, Grass, Lava, Subterranean	100%
Rough	125%
Sand, Snow	150%
Swamp	175%