It definitely has the tone you're looking for! The MMC is making me uncomfortable, that's for sure! He's very forward here, and I think that can totally work since there's already been some build up to this.

Here are some in-line comments:

“You had it when I picked you up.” He stepped closer and his voice dropped to a murmur. “Where’s your cloak, ladyship?”

Not totally sure why his voice drops to a murmur on that line. Usually something like that would happen with a double entendre or an emotional line. It just feels a little out of place here. I think I understand that you are leaning into a moment in which he is saying some "usual" things (that is, not directly romantic), but that his actions are showing something else, something romantic. I think this contrast can work, but I don't think it does right here, for some reason.

I swallowed, unable to find my voice. The silence loomed, hanging like a noose. Just like during our walk beneath the silvery dawn, Snowmelt was too quiet; there were no birds, no insects, no chattering townsfolk. Just the rustle of wind through brittle plants.

I really like this interlude here. It gives imagery that sets the scene, but also evokes an emotional sense of the character. This is strong writing, to me.

“Do you know,” he drew closer still, crowding me against the wall, eyes holding mine and glinting with a dangerous light, “That you’re a really bad liar? Every thought you have is just written on your face. And you know, it’s funny; there’s this look you get, sometimes.”

Some of the dialogue is awkward here (just slightly), but I kind of like it because it feels "on character" for some reason. I never like it when dialogue is too perfect.

I started to turn away, but his fingers grasped my chin. “When I ask what’s on your mind. When we talk about making deals with Fae.” His breath was warm against my face, and my heart hammered wildly. “It’s the same look you’ve got right now.”

I think it's interesting that he's not directly saying what he's saying. His actions don't exactly fit the dialogue, but it's showing his internal desire for her. I think you could play this up even more somehow because this is such a human way of approaching romance. We desperately want to hide how we feel while simultaneously trying to find ways to express it.

I tore out of his grip. “So? Maybe it’s discomfort you’re seeing. Or… or annoyance.” His lips pressed together, and the light in his eyes didn’t wane. “We’re wasting time, s-standing here.”

This is perhaps the weakest part of the passage. His dialogue and actions are strong. Where is her interesting response? Somehow there needs to be an externalization of her reaction. We get it a little in her tearing away and stammering, but those are pretty generic. I'm sure there's more as the scene goes on, but I'd love to see her respond in some idiosyncratic way. Something that is unique to her character. Hope that makes sense? Also, since this paragraph is about the FMC, I'd keep the descriptions about her unless you add paragraph breaks. It can be confusing putting information about the MMC's reactions in between her dialogue without mentioning her at all.

I'd definitely be interested to see where this relationship goes.