@JohnK gives an excellent explanation for castor - the horizontal offset between the steering axis and the tire contact point.
But maybe the question is about camber. That is the angle between the vertical axis of the tire and the vertical direction relative to the ground. The camber angle on the Connie's nose wheels is called positive camber, and an extreme case can be found on the tractors of that time. Curiously, it is a distinct characteristic only of US tractors like the John Deere (left) and Farmall (right) tractors below (picture source).
The reason is easier steering in rough terrain. As a tractor discussion board explains:
I have read that positive camber is intended to align the kingpin axis with the center of the tire contact patch. Supposedly this reduces the force required to steer the axle. If that theory is true, then changing the height of the tires would change the intersection point of the camber angle and the kingpin angle; it's improbable that swapping between, say, the correct R4 tires and the correct R1 tires for your tractor would make significant differences.
However, I am not convinced by the theory that the positive camber is there for steering ease. Here is why: I think it would be easier to roll a tire around in a circle than it would be to simply twist it, especially if one considers the tire will be pushing dirt out of the way as it twists.
I think the reason for the positive camber is to attenuate the camber thrust that can occur when the tires encounter uneven terrain. This would tend to help the tractor track straighter, and require less steering input to maintain a straight course. That characteristic, along with the caster geometry, should make the tractor track straight naturally, rather than tending to turn more when either a steering input is made or some uneven terrain is encountered.
The author of this post has his own theory; however, the point made in his first sentence actually has merit: Since steering in automobiles and European tractors is made easier when the steering axis runs through the contact point of the tire with the ground, positive camber is an attempt to reduce the steering roll radius of the twin tires which indeed should make steering easier.
Steering axis inclination reduces the roll radius in cars (picture source); since the sideways axis inclination could not be used in nose gears or tractors, both resorted to tire camber.