You do appear to be missing some stuff here. Here's how I'd handle your situation.
(As a foreword: bear in mind your players and the player characters being unaware of an aspect are two very different things, so you should make sure you distinguish between them.)
Entering the Scene
You said you entered a Forest with a River in it. The forest itself is pretty important, and you should probably have an aspect on the scene describing the forest you're in. If you also know for a fact there's a river, and it just wasn't mechanically important enough to be an aspect until now, you can just turn that fact into an aspect on the spot the moment anyone considers it important mechanically:
If you’re not looking for a free invocation, and you just think it’d make sense if there were a particular situation aspect in play, you don’t need to roll the dice or anything to make new aspects—just suggest them, and if the group thinks they’re interesting, write them down.
(This doesn't take an action or anything.)
You could either explicitly mention there's a Fording River, or just consider it implied by the Forest aspect.
If there isn't a river in the forest, or there might be but nobody's sure yet, you don't need to have an aspect for it. Your players or your NPCs can "discover" it later.
Creating the River
You would handle this very differently.
If there's a river aspect...
The characters might already know about it. It might even be a zone in the conflict! There's no need to "discover" it at all. People can begin using it immediately.
If the characters aren't yet aware of a River, it might not have even been significant enough to warrant creating an aspect for it. If it was that significant and they don't know about it, you're justified in asking them to try to discover it first. Normally you'd save this for bigger stuff, like the characters not yet being aware a recurring NPC is the Vampire Lord (but the players would probably know). This is just a small scene aspect.
If you didn't create a River aspect...
Your player can now Create an Advantage to "discover" the River, and create an aspect on the scene describing it. It was now retroactively there all along - but it only just became significant to the story. For the same reason, you might not worry about describing the small wildlife until someone throws nuts around and creates Squirrels, Squirrels Everywhere!! aspect.
This is your players' most powerful tool for just making things be the case in the world. Bear in mind: if they're in a desert, you'd be justified in making the discovery of a river a Fantastic (+6) challenge, or harder.
Using the River
Your Magical Tactician is at this point aware of a River, one way or another.
Nobody needs to spend any Fate Points to do stuff involving the River. The very existence of an aspect describing one means one exists, and people can interact with it. (Previous versions of Fate might have required a Fate point to use it, but not Core or Accelerated Edition.)
Your players might want to invoke the river (especially if they have free invocations on it), but this isn't required.
Now that the river exists: the Magical Tactician can go ahead and use a regular Create an Advantage action to freeze it and make things slippery. That's it! They can just do that now.
Here's a couple of things they may want to do with that Create an Advantage action:
Place a Slippery Ice aspect on the scene itself, allowing them to invoke it regularly around enemies near the river. They might have some free invocations on it to spend as a result of their Create Advantage action. However, the enemies might also invoke this one against them, too.
Place an aspect like Slipping on Ice or On Slippery Ice on a single enemy (everyone else will be unaffected). This now inherently means that enemy is busy Slipping on Ice or On Slippery Ice, and they'll have to Overcome that aspect if they want to stop slipping around. This might even mean they can't leave the river until they Overcome it - they're too busy slipping around to get away!
Your player may now invoke this aspect against that particular slipping enemy whenever they like, until it's Overcome.
Of course, the slipping enemy could also invoke it themselves: suppose that enemy rolled poorly on their defence, and their attacker is at +1 on this attack. The enemy could invoke their Slipping on Ice aspect to say they suddenly slip over, surprisingly helping them avoid the attack - they get a +2 to their defence roll, and their attacker is now at -1 and might fail their attack roll.