When I think of noir, I think about the following elements: crime, betrayal, temptation (often sexual), urban settings, pessimism, cynicism, and no-win situations. There's also a host of cinematic techniques that don't translate precisely into non-visual mediums, so I'll leave those aside for now.
Shadowrun has crime and urban settings covered, so that's easy. For pessimism, cynicism, and temptation, I'd look at my NPCs. Almost every one of them should reflect those traits in some way. They don't all have to be pessimistic; in fact, some of them should be defiantly optimistic, but that should be something other NPCs comment on. That'll bring home the point that it's a pessimistic world. And everyone should be capable of being tempted by something. Everyone has to have a price.
Betrayal and no-win situations are trickier, because you don't want to kill the fun of the game and if the PCs are betrayed all the time, they're going to wind up expecting the worst of everyone. This quickly turns into a game of turtle. I'd recommend having a fair number of missions that are the result of betrayal. In other words, the PCs should often be hired by someone who's been betrayed and who needs revenge. They're living in an atmosphere of betrayal rather than being betrayed.
Although it should happen to them once in a while. Don't avoid it all the time, by any means.
Finally, coming back to the visual stuff: play it up in your descriptions. It's raining. It's raining cold, bitter rain. The raindrops are exploding like a child's dreams on the cold, hard pavement. Well, maybe not that last.
AngryGM Says Something About This
Once your characters are obviously going to win, end the encounter/fight. That's tough, but I'm going to sum up what he said. (You should still read it, though) You need to figure out what the main question the encounter is trying to answer, and when the answer becomes obvious, end the encounter! Yes, I know AngryDM's advice talks about encounters in 4e, but you can apply this idea to 3.5e.
Flying Creatures
Open areas favor those who are mobile. Flying is a super easy way to be mobile. Use creatures with fly speeds! Is this a "hard counter" to your players? It can be seen that way. Especially if you have loads of them, because the increased mobility of flying creatures can make the PCs the slow ones!
Fight Fire With Fire!
Certainly, playing like a Mongol horse archer isn't something unique to your players. Other people would be smart like your PCs and would specialize in this tactic. This has the potential to make encounters sprawling things, covering very large distances, but that does happen.
Tower Shields, Terrain, and Spells
Grant cover from ranged attacks! Yay! A few people together could effectively block those archers. Terrain can grant cover, too, even in flat areas. Consider the great plains of the US. They are "flat," but not flat enough that a horse can run directly from any point to any other point. There ought to be variations and things to hide behind. Additionally the flat(er) terrain can give someone on top of a modest hill the chance to spot the PCs coming.
What about clouds of fog? Firewalls? Those are all things that can shut down this fighting style. If your villains know the party, and truly wish them harm, they will employ tactics and set up ambushes where the party will lose their mobility. Palisades and ditches can be used in place of magic.
Consider the Hard Target
Additionally, this hit-and-run style is really bad against "hard targets" like castles, forts, and other entrenched positions. Sure, you can scare the defenders inside, but you need more than arrows to break it. These could very easily require the PCs to (gasp) dismount!
Best Answer
0. Do your players want this, too?
If you haven't discussed a different playstyle I think they're reasonable to still expect the "sporty" style you were previously playing. That's why I think--even one session in--a change like this would be equivalent to starting a new campaign: same setting and same characters, but different game.
If you have not had that conversation, stop reading here. Talk to your players. If they agree on a new style, proceed:
1. Do it to them. Before you do it to them, tell them you're going to do it to them. And tell them while you're doing it.
"The hobgoblin captain has arrayed his shortbowmen on inaccessible ground and they're ducking behind full cover after each shot. Man, this is just a killing field! So, Gary, what do you do next?"
"OBJECTIVES, TERRAIN, COVER, VISIBILITY" are the four words I have written on my gm-facing side of my table tent. Use these to your advantage, and teach the players to use them to theirs.
2. Design your world, not your encounters.
Think about the people in your world, where they might exist, and what they value. Array them as makes sense in a world without your PCs. Do the encounter math as suggested by the DMG. Then don't modify anything!
Now you have a range of possible encounters including (a) not worth even acting out--just declare victory, (b) cake-walk, (c) very easy, (d) easy, (e) medium, (f) hard, (g) deadly, (h) superdeadly (would be deadly even at APL+1), (i) superduperdeadly (deadly at APL+2), (j) death sentence (could kill the party before they even act).
I'm not kidding: "no," "cake," "VE," "E," "M," "H," "D," "D+1," "D+2," and a frowny-face with two exes for eyes are notations next to possible encounters on the mind-map of my current adventure.
Now that you've got this in hand, you are prepared to properly describe the encounters as they happen. In a "cake" encounter your barbarian's axe cleaves enemies in twain (doing 9 dmg); the same hit in a D+1 encounter manages to annoy the enemy. But if you didn't do the homework, you're going to properly convey to the players the crucial information their characters would know: "we're in over our heads, here, and will be lucky to get out alive."
3. Help them find their way to spectacular victories.
There are many gm-styles and I'd naver say one is 'right' or 'wrong.' But if you're looking to help a group transition their style--or to learn a new style--I suggest that the one I call "find a way to 'yes'" may be really useful. In this approach you are explicit about asking players not only to describe their actions, but also their intentions. You work with them to craft their actions so that they to progress toward their objectives.
You don't have to pull any punches in combat or in their opponents' preparations and they don't always have to succeed. But this way their efforts aren't impotent even when unsuccessful. Failures aren't a matter of "the gm screwed us over," but are a matter of "the kobolds screwed us over." And successes can be spectacular. Like Hannibal says: "I love it when a plan comes together."