The "forward" in "fail forward" means "motion", not "progress".
So, you may be familiar with games that don't do anything special on failure. You line up to make a roll (like an attack roll) that generally does nothing more than succeed or fail, and when it succeeds you can change something (like deal damage) and when it fails nothing happens. Often you're making these rolls in some kind of overarching framework (like combat rounds with initiative) where failing a roll and "losing your turn" means something else gets the chance to do something nasty to you before your turn comes up again (like a marauding ogre tries to club you into next week).
When play has moved beyond the scope of an overarching framework in one of these games, you can falter a bit by trying to play like there's still a framework there. If you fail and nothing happens, what happens before your turn comes up again? Does nothing happen? Do you get infinity turns? So why are you rolling? But this is still hard, shouldn't you be rolling?
"Fail forward" is a philosophy to approach these situations that basically means: don't present the same game state twice. Every roll, success or failure, changes the state of affairs somehow so you can't just loop back and try the same roll again for the same stakes.
Dungeon World can have a pretty easy time of this because you're not always making a roll explicitly to try to accomplish something in the game, but rather because if you do it, you do it - you've set up a situation in the game fiction and there's a move that comes out of it. You're climbing up a chain to a wizard's tower despite the threat of the rain, the moss, the looming drop - that's defying danger. On a 6- the move may not say anything at all about what happens next - as the GM, you're given free rein to change the game state.
Because there isn't one fixed thing you have to do, picking a response is an art you'll have to develop. I mean, you still have to make a move that follows, that hasn't changed, but you don't have to make a move that follows strictly along the narrow slice of intent that is the chain, the rain, the moss, the looming drop. You can follow something else in on a collision course. You can follow, among other things, your prep.
Exploit Your Prep
Even if this is the first session you should still at least have some ideas sketched out about the wizard's tower as a whole. If the wizard's tower is largely an unknown quantity to the players you can start developing those ideas out at them. So.
The wizard's tower is a derelict, its guardians and wards as dangerous as its squatters and malfunctions? You might want to separate them:
You lose your grip for a second, Fightgar, but after a brief kicking scramble you manage to secure it again and keep going. It's not until you've gone a few more links up that you hear the sound of shearing metal and realize your boot went almost cleanly through a corroded length of chain. The tower is straining at the chain, buffeted by the wind, held in place by a single link rapidly being bent in two.
So, uh, everybody else? If you wanna get up there with Fightgar, you ain't got long to try.
Or show a downside to their race, class, or equipment:
You lose your grip for a second, Fightgar, but after a brief flailing scramble you manage to secure it again. But, uh, you know how metal exposed to the air builds up an oxide layer to protect from corrosion? Magemetal exposed to reality builds up a similar layer of normal, and you just tore a big chunk of it off. Your family's ancestral warmaul is suddenly and sharply attracted toward the chain like a magnet, basically stapling you in place. It's all you can do to keep it from crushing you.
The wizard's tower is a place of evil, full of prying eyes and bound demons? Sounds like it's time to show signs of an approaching threat:
Your feet lose purchase and you drop, Fightgar, but you're able to hang on and swing yourself back up with great effort. You think you heard something click somewhere? Like, loud, sharp, and clear, but nothing more seems to be happening...
And let's cut away for just a second to the inner sanctum where you're center stage of a crystal ball climbing up, the rest of the party in view at the base of the chain behind you. A withered hand parts the gold and blue robes of Goldor the Blue and rests against a shimmering red field that extends out of view. "Ah, Archibald, we have visitors! Strong visitors. Archibald?"
Cut to black. "Go play." There's the sound of a force-screen being dispelled, then a frenzied, otherworldly scream.
Or maybe you can just deal damage (v1):
You feel yourself falling and make a sudden, frantic grab at what seems like a loose link in the chain, that rattles around for quite a bit as you finally find purchase. When you look up to keep going, you notice a summoning sigil in the chain ahead of you and a spindly little demon the size of your fist standing right in the center of it. He startles, turns, and yells something up the chain, and sigils start lighting up.
The same yelling's coming from below you too. You look down and, yup, demons there, too. Unless you understand gutter-demon it's not going to make a lot of sense. Mostly gibbering but they seem to be saying the word "chain" a lot? You infer from context, and also from the needle-sized spears they start pelting you with, that they object to your presence.
Each spear isn't a lot, but they've got numbers. Let's say three swarms of numbers? Take 1d6+2 damage, but you've still got your armor for now.
The wizard's tower is mostly benign, but the wizard just wants privacy? Okay. You could offer an opportunity that fits a class's abilities:
You are almost entirely sure, Fightgar, that this chain is somehow animated. You cannot conceive of how you could have failed to grab it so consistently and so precisely that you end up suspended upside down, arms and legs through the center of the links, and a bit pained by the position but not even really hurt.
Certainly Shanksworth is going to have to extract you from this like he was disarming a trap. Unfortunately, what more Shanksworth thinks is entirely up to Shanksworth.
Or perhaps use a monster move (seize something by force):
You swing all your weight over to one of the links in the chain and feel it... rip free? Frantically you make a grab around and manage to secure yourself, then look down curiously to see where the link fell, since the chain seems intact. And it hasn't fallen! It's just tumbling down the chain, end over end, like a conjurer's trick. Then it smacks into the ground anchor, which rings like a gong.
"Hey, hey, hey, hey, hey!" echoes a voice up a sinkhole next to the anchor. ...was that there before? A towering form climbs its way toward the surface and vaults out to land with a stomp. It's an ogre! In the blue-and-gold livery of Bluedor the Gold! ...man, this is maybe the best-fitting clothing you've ever seen on an ogre.
One hand closes around the chain. "Big wizard, he say no visitors today! So you gonna stop climbing? Or I gonna make you stop!" He rattles it from side to side and by the time the wave reaches you, you can barely hold on. What's your play here?
You don't want to play your hand about the wizard's tower yet? Yeah, okay. So there's nothing extra to copter in about their progress on the chain, so just extract a price from them on their way up. You could use up their resources:
You lose your grip for a second, Fightgar, and almost go tumbling, but after a great effort of strength you flip back up and finish the climb. When you're taking stock afterwards, you realize to your dismay that you never fastened your pack properly! Or maybe it popped free when you did the 360. You're not sure.
You are sure that you're going to roll 1d6 3 times and lose a use from that slot in your pack, though.
Or consider dealing damage (v2):
You lose your footing, Fightgar, and for a second you're suspended there by one arm, the ground swinging beneath you - but then there's this rush of adrenaline and you lever yourself back up onto the chain and push yourself forward, just go go go go go! And then you're up at the top of the chain! ...and after a little bit to collect yourself the adrenaline rush wears off and the pain hits you, just ow ow ow ow ow.
Mark the "weak" debility. If you have, like, an hour to hang loose and collect yourself you can clear it, but spoiler alert, you might not be getting that hour any time soon.
And yes, Fightgar's up at the top of the chain, but Fightgar didn't succeed. Not on any scale that really matters. I mean, you don't just make the first roll of the play session, say, "wow, that was everything I wanted out of this! Good game!" and pack up and go home, right? There's more to it than that. There's something Fightgar wants to do at the top of the chain.
Countdown to Destruction
So let's go back to your prep, where you thought about the wizard's tower. There's a reason the PCs are at the wizard's tower in the first place, right? They want to confront Goldor the Blue. They want to seek the counsel of Bluedor the Gold. They want to claim the lost Orb of Bluegold from its last resting place. And you've come up with a way to deny them that without killing them.
It's called the impending doom, but it's not the end of the campaign; it's something bad that will happen if the PCs don't stop it. Goldor the Blue completes his vile ritual and descends to the hells to muster a conquering army. Bluedor the Gold finishes preparations and departs for the end-of-edition climactic metaplot battle; tomorrow, he will never have existed. The tower finally disintegrates and its treasures are scattered across the trackless wilds.
You've got a list of steps to get there too, grim portents to show the PCs things are getting more dire, in addition to perhaps an actual visible countdown clock so the PCs can see that Bluedor's preparations are at 3 o'clock out of 12. Even if you don't directly impose doom advancing as a consequence, introducing unexpected complications gives it more chances to come up.