Any single-engine prop plane is going to exhibit turning tendencies, which are most pronounced at high RPM/torque and low speed. In the western world, most props turn clockwise as viewed from the cockpit, which produces left turning tendencies.
The three left-turning tendencies we primarily deal with in the tricycle-wheel world are P-factor (or asymmetric prop loading), torque (opposite direction of rotation), and spiraling slipstream (hitting the left side of the tail amongst other surfaces). In tailwheel aircraft, you also have gyroscopic procession turning the nose left at the moment the tail raises.
There’s also the weathervaning effect, which causes an aircraft to want to point into the relative wind. This is also much more pronounced in tailwheel aircraft.
That said, these tendencies are all fairly easy to overcome, but it requires touch and attention to the rudder pedals, which are linked to the nosewheel by bungees in some aircraft, and in others it is free-castering (and in much larger planes, independently steerable).
There is no separate steering control for the 172 - you steer with the pedals, and there is a cam that locks it straight ahead when there’s no weight on it, but it’s otherwise not manually lockable. The pedals alone will steer it up to 10°. You can also use independent braking to steer, but usually only when taxiing, and the nosewheel will caster to 30° when using differential braking.
The 172 will handle most crosswinds fairly well. The max demonstrated crosswind (meaning what was flight-tested during certification) is 17 knots, however, it can do more, but most pilots opt to establish personal minimums at lower crosswinds. But at some point in the crosswind spectrum, you run out of control authority and it becomes nearly impossible to maintain the centerline. It can get squirrelly and lead to a ground loop or loss of directional control if you’re not careful.