Granted, this particular bike might take some heavy leaning to make anything like a turn, but for a snow bike, that might not even be such a bad thing, since... that's not what these vehicles are about in the first place?
You pivot the front wheel to turn, the leaning is secondary. It's to counter centrifugal force so you don't fall over.
Edit: I'm mistaken and didn't account for camber thrust which happens when "a point on the outer surface of a leaned and rotating tire, that would normally follow a path that is elliptical when projected onto the ground, is forced to follow a straight path while coming in contact with the ground, due to friction. This deviation towards the direction of the lean causes a deformation in the tire tread and carcass that is transmitted to the vehicle as a force in the direction of the lean." https://en.wikipedia.org/wiki/Camber_thrust
But, in-fact at speed, while pivoting the wheel will initiate the lean, the lean itself is the primary factor in steering the bike.
These weird unintuitive mechanics, are part of why learning to ride a bike with training wheels, or from a tricycle is so hard, the steering mechanism of a bike inverts from when there are 3 wheels on the ground, to when there is 2 wheels. And also a significant reason that "Balance bikes" have replaced a lot of tricycles and training wheels when teaching kids to ride a bike.
Balance bikes aren't even all that necessary and a lot of them are so poorly made that they aren't doing much of anything. Get a decent real bike of the appropriate size and take the pedals off of it (lower the seat so they can sit while both feet are flat on the ground).
Teach the kids to glide. That's it. Start with gliding a few centimeters and work up to gliding multiple meters/feet. Go at whatever pace is comfortable. It could take months or minutes. You'll know when the time is right to put the pedals back on and raise the seat. At that point, you are 5-10 minutes max from riding a bike like a pro.
For my oldest kid, I paid $50 for a "we will teach your kid to ride in ONE HOUR" class and watched them teach it (my kid took 45 minutes). Since then, I've taught little kids, older kids, adults. This stuff really works. It is seriously hard to believe that the old way of teaching people to ride bikes ever existed.
The gliding is definitely the skill needed. It helps to have somewhere with a slight incline like a driveway apron too. At least it made it less boring for my son. The problem I see with the gliding is that it wasn't all that interesting to my son. So it really took him to get old enough to realize it would be a step towards riding a real bike.
What I can't believe is that the high end companies like Specialized, Trek, etc hadn't figure this out years ago. I can't believe they even still allow themselves to sell bikes with training wheels. I get that it's a short term sale for parents who don't know any better but you'd think they'd be better off if the kids actually learned to ride quickly and graduated to bigger bikes instead of maybe never learning to ride until much older.
They should sell the bikes with the crank arms that can pop on and off with a quick release and without actually taking off the front sprocket. Even taking the pedals off the crank arms are still in the way.
At least that is what i got from Flick of The Wrist, a kinda funny instructional video on riding bikes (it's on youtube) :)
I have a cargo bike with a lockable front wheel, and even if I forget to unlock that, I can still drive, even though it's unpleasant.
That unpleasantness mostly comes from being unable to turn my front wheel in the opposite direction before leaning in to the actual turn direction, though.
This is on a manually powered bike, though, so maybe things are different on a motor bike? But I sort-of doubt it, since the physics are the same...
Bringing this back to the original post. Looking at this thing, I imagine it'd be hard to properly lean it given what appears to be significant heft.
Edit: To be clear, I mostly agree that it's the lean that's the primary factor in the turn. Just a subtle bit of confusion over how important steering is over initiating the lean in heavier bikes.
Turning the front skis (which have a range of, maybe, 20 degrees, not sure, never used them!) is discouraged, and probably doesn't do much, except in emergencies. Like braking!
And yeah, these things weigh around 200kgs (450 lbs), before occupants.
Secondly, at lower speeds and higher turning radius' bikes do in-fact steer with the front wheel, counter to their lean. Often encountered while navigating a parking-lot for example. I imagine an All-terrain bike is more likely to be needing to operate more often in this envelope however, so am also a bit confused on how it's anticipated to work.
Mostly, you'll use your snow bike to go fast (60-100 km/h, 40-60 mph), and you really want to plan your trajectory pretty well at those speeds. Using your handlebars, or your 'brakes' just isn't a realistic option!
Sure, if you want to turn left a bit: lean heavily left, and steer slightly right. And vice versa. But making any sudden turns? Not going to happen, especially not with a passenger...
Having said that, it's 100% the case that a 2 wheeled bike with rounded tires in a lean will turn. Just consider that the circumference of the tire shortens as you approach the edge, it must travel a shorter distance per revolution. so without sliding, it clearly needs to turn.
In-fact, at speed, the lean of a bike is the primary factor that contributes to the turn.
Now, for wider turns, you do need to turn your front, but even then, it's usually in the opposite direction!
Anyway, on snow mobiles, you really don't want to need your steering handles, as they don't control a wheel, but skis! And staying on the trail mostly involves reducing speed and, well, leaning. By the time you really need your steering handles, or your brakes, you're really already in trouble...
In all likelihood you are doing it unconsciously, generally, as one goes to initiate, say a right-hand turn, as you begin to lean right, you also apply a slight additional pressure to the right handle bar, which steers the wheel to the left, this initiates counter-steer which leans the bike to the right. With a stable bike, and a fixed front fork, it would be exceedingly difficult to initiate a lean significant enough to navigate most roads at the speed that we do.
If I forget to unlock my front wheel, I can go about my ways just fine: it's just unpleasant.
I also ride snowmobiles on a regular basis, and if you require any effort at steering (like at braking!), that's pretty much an error: you shouldn't need to do it! And that's even at 60km/h...
Also, I'll be honest I haven't ridden a snowmobile in so long that I don't really have a mental model of it. I'm interested though, Do you think they are a similar experience? Don't they normally have like many more points of contact?
Still, the experience is exactly the same as a 'manual' bike (here's mine: https://www.gazelle.nl/puurnl).
Point is: you need to really steer beyond leaning? You either hit a over-40-degree turn (not uncommon even in Amsterdam!) or you did something wrong. You need to brake? Either an idiot crossed your path, or you definitely did something wrong!