Yes - it’s rotated about the vertical axis (yawing) so the direction travel stays on the runway heading even though the nose is pointed off left or right into the wind. About the moment of touchdown this is cancelled out to hopefully make it go straight down the tarmac:
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Overcorrect on landing though and it can give the tyres something to complain about:
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Broadly speaking you are correct, however there are couple of things worth mentioning.
There are actually a few techniques for landing in a crosswind which can vary slightly according to aircraft type but most commonly as you've mentioned, as you come over the runway threshold with the aircraft nose pointing into the wind and thus, not aligned with the runway, you can then use the rudder (in or just before the flare) to rotate the aircraft nose to align with the runway (de-crab). This however, particularly on swept wing aircraft, causes the airflow over the upwind wind to increase, causing a subsequent increase in lift on that wing. Essentially you notice this as the downwind wing dropping and you need to quickly counter this with ailerons to keep the wings level throughout the flare and touchdown. This may (or may not) be a point that investigators look at.
Also, using the above technique to early can cause a sideways drift of the aircraft during the touchdown which can cause it's own problems.
In addition the runway condition also plays a role in how the landing is conducted. This is aircraft dependant and I'm not familiar with the CRJ however, if the runway is contaminated (or in this case slippery), you may elect to touch down without using the rudder to correct to nose into wind until the wheels are firmly on the ground. You basically rotate the aircraft in yaw on to the runway centreline as you de-rotate the aircraft nose back onto the runway. The B737 for example has castoring main wheels which allow you to do this up to the crosswind limit of the aircraft. (Although most companies don't like this as it gets expensive on the tyres)
The reason you may want to do this is it's easier to make a firmer landing which is something you want to do on a contaminated runway (make the wheels break through any contaminant and contact the runway surface), also using the above crosswind technique can cause the flare to become prolonged which you want to avoid on a slippery runway, where landing distance can be a factor.
There is a another technique which is to fly the latter part of the approach with crossed controls (sideslip) but I've never really figured that one out.
I've been sent a video from a friend, filmed from the flight deck of the aircraft at the holding point, waiting to cross or line up. (Subject aircraft travelling left to right). I can't link due to expletives, but I'm sure it'll soon be in the public domain sooner or later if not already.
When the aircraft was filmed through the captain's window, the aircraft appeared to have a slight nose up attitude. As the camera pans past the frame between the captain's and FO's window, the aircraft then appeared to have a nose down attitude, and as you suspect, a sudden full upward elevator deflection less than a second before impact.
E: The video also indicates there was a significant headwind, perhaps slightly crossed from the right, judging be the way the snow is being blown.
E2: the METAR at the time of the incident:
CYYZ 171900Z 27028G35KT 6SM R24L/3000VP6000FT/U BLSN BKN034 M09/M14 A2993 RMK CU6 SLP149
In the initial part of the video everything looked normal to me, and I couldn't really tell how things exactly went wrong at the last minute however I watched on my phone so may have missed some details. It does look like all three wheels touched down on the runway at the same time, which may indicate a hard landing.
I believe the landing was on runway 23 which gives a crosswind of 18Kts gusting to 23kts. It's difficult to say since I don't know the runway condition, or the aircraft or company limits but it could be close to the allowable limit.
