No, that's actually not true. Hitting Ultima-Thule is much harder. For starters, just figuring out where U-T actually is is very difficult. The observations we have only constrain two of its three degrees of orbital freedom. The third has to be inferred via orbital mechanics. Likewise, figuring out where the spacecraft is is also non-trivial. By way of contrast, figuring out where you are relative to New York to within a meter of accuracy is, nowadays, a simple matter of switching on your GPS receiver. (Even without GPS, all you need is inertial guidance that is stable for half an hour or so. That's much easier to achieve.)

Finally, there are unpredictable orbital disturbances. N-H uses thrusters for attitude control, whose effect on the trajectory is not entirely predictable. (c.f. https://en.wikipedia.org/wiki/Pioneer_anomaly, which was only detectable because, although Pioneer had thrusters, they were turned off for long periods of time).

I know these things because I used to work at JPL. There are entire teams dedicated to spacecraft navigation. The stuff they do will blow your mind.

"They don't have to deal with unpredictable atmosphere"

Well, no, but they do have to deal with an atmosphere that has, until they get to it, only been theorized about, never observed - which is not the case for the atmosphere above New York.

There have been precisely four spacecraft that have gone anywhere near so far out as New Horizons, and they are between them the source for the majority of data we have about the atmosphere in the outer solar system. One of them discovered an anomalous acceleration effect that confused scientists for decades (and which, while it turns out not to have been externally caused, certainly left scientists wondering for a while whether their model for the solar wind was accurate). Of those that we believe have passed through the termination shock of the solar atmosphere, none have yet returned much accurate information, so we actually don't know much about the conditions there. I don't mean to say that these effects have meaningfully impacted navigation for deep space probes, but more these are genuine voyages of discovery - where they're going is predictable but until they get there we really don't necessarily know whether our predictions will be accurate.

Spacecraft also do some corse corrections. You can also measure where your going very accurately averaging over a few hours.

They do have to deal with accurately determining the target destination, especially so in this case.

I believe New Horizons did course corrections, even fairly late.