I know you wanted to exclude terrain alteration, but I'll bring up
Vantage Master since water can impede or improve the mobility of certain units. You can summon four different elemental types of units. Water Natials usually move very slowly over land, but way faster over water. Your chosen master can cast a magic spell that can raise or lower the water level, enabling your water units to travel further (or to landlock an enemy master's navy).
Not all maps have lots of water like the meadow map. Some maps have little to no water, so raising the water by one tile does allow you to spawn and move a navy of water Natials around.
In
Pokemon, some Pokemon and abilities alter depending upon the current weather and IIRC the environment (the battlefield background being determined by what tile you were on when you entered battle). I may be mistaken.
In
Guild Wars 2, some of the Ranger pets you could get had the ability to dig up different objects on the ground that you could then walk over to pick up and use, ie like a rock to throw to stun an enemy or feathers to throw and blind them.
In
Aselia the Spirit of Eternity Sword, each node/tile on the map had different elemental magic stats that would act as modifiers in the battles on top of them, and every unit in the game had an element. Most of the time the modifiers were too trivial to care about like +10% green or -20% red, but IIRC there were a couple of sections (I think the invasion of Malorgian in chapter 3, and maybe the invasion of the Southern empire in chapter 4) where you could notice that some tiles had some pretty significant modifiers like +50% blue that you could play around with by deploying blue spirits and trying to avoid sending red spirits onto that tile if it is being defended by enemy blues.
Elemental modifiers on this spot with two enemy squads I'm attacking. The modifiers are rarely this high.
In the
Trails games (namely the Crossbell duology and the Trails of Cold Steel pentalogy), there are 7 elements. The four elements of water/earth/wind/fire pervade the world and are present in the baseline turn order bonuses. However, sometimes you will be sent into some sort of dungeon or some region wide phenomena will happen, bathing the area in the magic of the three higher elements of Time/Space/Mirage. Gameplay wise this means that some unusual turn order bonuses will show up in battle that you want to be on the lookout for like 50% heal for whoever snatches it, losing all of your CP for whoever snatches it, spells costing 0 EP for whoever snatches it, deathblow, etc.
Final Fantasy XI and
XII: the current weather condition (which can vary by region) can improve or dampen the power of elemental spells. If you cast a fire spell during a heatwave then it will be more potent than if you cast it during rain. I don't recall how strong the modifiers were. In FF12, rain sogs up bowstrings and makes bows and crossbows less effective.
In
Final Fantasy Tactics Advance 2, the Geomancer job can use different abilities depending on what tile they are standing on or the present weather condition. If they are standing in snow, then they can cast the avalanche spell.
Valkyria Chronicles 1 & 4: each character has a few unique traits, such as chatterboxes getting lower stats when standing near other party members. IIRC some of the traits had to do with terrain, like nature lovers being hit with a massive stat increase if they are on a paved road, or nocturnal where they get a stat boost at night, or veggie-maniac.
