
So this smartass Seungho didn't notice that the footprints were too big and deep for being Nakyum's. Also he could have followed them. They are all smart in this story i guess, the assassin first deciding to kidnap the guy (instead of immediately kill him as he did with the servant no one cares about) while snowing and leaving clear traces.
In Seungho's chamber Nakyum would have been safer, and SH could have kept an eye more easily, but the author had to create the unpteenth misunderstanding for drama reason
btw when he was kidnapped, they were at the doctor's house, it's also just a coincidence the assassin found Nk awake after the sex, there are actually a lot of plot-holes

It's not clear if he saw those things yet since we only know that he's keeping Na-Kyum in a secluded area. I see a lot of comments asserting things that haven't happened yet. This is why I only stated that I hope Seungho is sharp enough to notice all those things, because his character is also that which loses his temper very easily. However, in his defense and towards my theory, he didn't act out like he wanted when he first saw Na-Kyum laying there. His hands could have gone around his neck or caressed his face, but he did neither and instead walked away only to have given the order to never open the shed door and therefore appearing in the last panel; standing watch over a sleeping Na-Kyum. I can only suspect Seungho needed time to think some things through without disruption...which is probably a crude way of rationalizing why he put Na-Kyum in the shed.
The assassin has been watching Na-Kyum for an opportunity. Remember he actually had that one servant watch him in order to lure him outside, but that guy didn't work out. So he got rid of him. I wouldn't call it a plothole if you're counting on someone to care for a lowly servant that was practically dismissed of his duties by a noble. In context, no one would look for this guy. Na-Kyum however is different. The assassin is a seasoned professional and could read Jiwon's jealousy. He knew Jiwon didn't have it in him to kill someone. He's just someone who's heartbroken. That's why he only kidnapped Na-Kyum and told Jiwon of the things he could do to get rid of Na-Kyum. This is why the assassin simply left Na-Kyum somewhere where he could be found.

We know for sure he didn't immediately notice the difference in size of the footprints, and SH being an experienced hunter should have known those traces couldn't belong to Nk. I think he had enough time to rationalise it's impossible NK escaped.
The assassin acting as a morality pet for the noble who looks down on people like him but still killing a servant in cold blood is a bit hypocritical...it's clear he only kidnapped and not killed him because of plot reasons. Jihwa paid him for killing an innocent and for stupid reasons like jealousy, so he showed for the start NK's life wasn't even worth for him, why the assassin should care for a noble's morality and guilt?
The plot-holes are the footprints, a seasoned assassin deciding to act when it snows (so it's easier to be traced-down) and when Seungho was close to his target (he could have woken up, I assume NK cried when the killer caught him?) , a seasoned assassin talking with his commissioner in front of the victim and then releasing him...unless NoName thinks Nakyum will never talk about the kidnapping (he probably heard Jihwa's voice too) or that he will never be believed, but this means that saving Jihwa's morality will only lead to Nakyum being hurt. C'mon this kidnapping plot was poor planned and pointlessly dragged for several chapters and its only reasons were to create another misunderstanding between the main characters and a fanservicey side-ship.

I disagree with believing this arc didn't amount to anything besides another hate-sex scene from Seungho. I think this arc provided a few things for character development, especially for the relationship between Seungho and Na-Kyum as well as settling Jihwa's feelings for Seungho. After all, this arc wasn't about the assassin kidnapping Na-Kyum, it was about Jihwa's jealousy and how far he will take those feelings.
During the time Jihwa had to wait we saw:
Na-Kyum trying to run away and giving up.
Na-Kyum giving in to the words of his teacher and letting Seungho have his way with him.
Seungho investigating the reason behind Na-Kyum's obedient behavior.
Seungho realizing he doesn't want obedience from Na-Kyum.
Seungho realizing he's captivated by Na-Kyum.
Seungho trying to deny those feelings to his peers.
Irate servant treating Na-Kyum badly (talking down to him, putting rocks in his food, ultimately attacking him).
Seungho lashing out if others touch Na-Kyum.
Jihwa having a nightmare where Seungho hates him for killing his lover.
Jihwa being told by Seungho to stop obsessing over him.
Seungho confesses (both unknowingly and knowingly) his feelings to Na-Kyum.
Seungho realizing that this is how Jihwa must have felt for him.
Na-Kyum gets kidnapped.
I think this kidnapping was a catalyst towards Seungho's and Na-Kyum's relationship and not the main reason for the second season itself, even though we all wondered what would come of it. I think the main reason why people felt a bit off by it was because people were expecting this big heroic climax where Seungho comes to Na-Kyum's rescue.
Na-Kyum is a low born, while Seungho is a bi-polar noble with trust issues...he's far from a knight in shining armor. He's used to pleasing himself, first. He's just now learning what it's like to love someone. He's never been heroic nor has he been raised to come to anyone's rescue, so that will never happen until he comes to the full understanding that it's fine to do.

More than half of the things you mentioned would have happened anyways without the kidnapping plot, which was clear from the start would have failed. The only result of this plot is Jiwha giving up with his feelings for Seungho (unrealistic after the fresh and most painful rejection) and a new, cliché side-ship
Seungho isn't telling people what he suspects. I mean, it would be in pure Seungho fashion to act out of jealousy and possessiveness if he acted out of rage and just locked Na-Kyum up to imprisoned him, but Seungho is also very sharp. Na-kyum would willingly leave a shoe behind as he tried to leave Seungho, and then faint on some mountain trail while still warm?
I can only hope Seungho puts two and two together in thinking this is weird. He should know Na-Kyum's habits if he tried to leave, just like he should know how warm he would be if he made it to the mountain trail and fainted.
I think he didn't let anyone talk to Na-Kyum, not because he's punishing Na-Kyum, but because he can't trust his servants for the time being and needs to get the story from Na-Kyum before he's convinced to not say anything. That's probably why he's keeping a close eye on Na-Kyum in that last panel.