Depending on the nature of the fight, it could go a few ways.
I think Snark Knight you have described the situation where Carlos is sent to tell Harry off and it devolves into a duel. Depending on if Harry was being rational or not would be the decisive point. Harry as a raging beast is terrifying, sure. But he tends to win more fights when he is being cold and rational. Which I think is intentional on Jim's part. In terms of mechanics I think you are right pretty much, I think Harry could counter with things Carlos might be underprepared for. Like black magic - i.e. mind assaults. He might even be desperate enough. He could also attempt to just out-muscle Carlos in some way, because Carlos is weaker. And Harry is far more formidable in close-quarters due to his Winter Knight power.
Jim has sort of been a bit evasive on how water magic works, he often says it's a fairly passive or reactive form of magic. But then he shows Carlos wiping the floor with his entropy stuff. If Harry had learned some water magic from River Shoulders, he might be able to counter Ramirez more effectively. Just as fire can be extinguished by water, enough heat can vaporize it. They are each others counter in a sense. I think ice magic might be his best bet, as Carlos uses entropy a lot (disorder) so Harry might want to use energy (order). I know it seems counter but he might just be able to lock Ramirez down with it. Carlos also has horrible physical injuries that Harry could exploit. And if Harry had learned some shapeshifting from River Shoulders (maybe with some tips from Grey), he also might be able to use that to his advantage.
There are scenarios where it isn't just the two of them of course. Ramirez might have a team of Wardens, maybe including Luccio. Maybe even including Senior Council members. That alters things dramatically, tactically speaking. Harry might be alone, or in his Castle, or have Bob, or Mouse, or the Alphas, or Ebenezar (with or against), or some Winter Fae, or White Court Vampires, or Molly etc. Any combination of these would be interesting and require vastly different tactics. If the might of the whole White Council and their allies came down on Harry (like they did with Kemmler), unless Harry was fairly upgraded and had all his new allies (some of which are also supposedly White Council allies) Harry would get smashed. Jim has stated that a few times. Which isn't to say that there isn't a scenario where Harry wins either, but I suspect the Council would already be fragmenting and Harry would shatter them at their worst moment. I think this is what the Gatekeeper was referring to when he hinted at "Harry's hour".