Is the duke of Weselton one of the villains in Frozen?

His ডিজনি Wiki page is pretty good, actually:
link

Here, he's considered the "secondary antagonist" (Hans obviously being the main antagonist).

Here is a section of his "trivia" from the ডিজনি Wiki page:

While selfish, greedy and pompous, the Duke is not actually completely evil, since he cared for Anna when she returned, and he's very shocked when Hans told them Anna was dead. He is simply one of Hans' pawns, since he was lied to and manipulated. However, he did order his bodyguards to assassinate Elsa even without Hans' knowledge, which earned him his punishment of being cut off as a trading partner of Arendelle at the end of the movie.

The Duke is a red herring. At his first appearance, he reveals himself to be wanting to "exploit Arendelle's tradable goods" in a monologue. He follows with "Did I say that out loud?" This makes the viewer believe he is the villain, even আরো so when he calls Elsa out for sorcery, and again when he sends his goons to kill the queen. However, the whole time, he is merely a cover-up for the real villain Hans.

Thought you'd find that interesting, and hopefully it's helped to answer your question.

Of course, some people might say that Hans is the only villain, and others might say that both characters are equally villainous. Personally I like the idea of calling Hans the primary villain and the Duke the secondary villain though.

My opinion on him is not very জনপ্রিয় yet but I still think it is the truth about this character
Now what makes him a villain?
"Ahhh Arendelle, the most mysterious trade partner.. Open those gates so I may unlock your secrets and exploit your riches"

This is basically his goal from the beginning til the end and he has a way of doing it... Use Elsa's secrets against her.
Basically this guy is much আরো evil than আপনি thought. Of course that Hans is the main antagonist near the end.. But the Duke totally had enough stage to be what's called "the central antagonist" and therefore the most threatening one.
When আপনি look at চলচ্চিত্র like Monsters Inc অথবা Cars 2, আপনি see the villain in the end isn't really the most threatening one but only the one who has the most ambition.
Cars 2 - Miles let's Professor Zundapp do the work for him freely, but he does not take direct involvement in the plan, despite staging everything and giving quite a প্রদর্শনী with his disguised voice
Monsters Inc - Waternoose hires Randall to install the scream extractor to solve the company's crisis, but doesn't directly fight অথবা hate the heroes. Randall even tries to convince him that Sullivan got what he deserved.

Back to Frozen, The Duke is kind of the same as in these two Puxar movies. He wanted আরো power, আরো money.. he basically started the whole thing দ্বারা incriminating Elsa for money!! Hans in that stage was an opportunist without a door open for him, meaning he still had to be a hero of some sort and stay out of trouble.
I don't think Hans came that evil, he was rather conflicted at that point. He had 12 big brothers laughing at him so it's natural he came with intent of starting to live a happier life yet the সিংহাসন was still very tempting and his actions and manipulations were inexcusable. But he didn't fight the নায়ক directly until the last 5 মিনিট of the film.. while the duke did kuch worse things. His worst crime was attempting to assassinate Elsa for power and money. A guy who plays pretend and says out loud that he wants to be rich and dominant.. sends two thugs to the dangerous zone of the arctic with Hans protecting Elsa's life at that point.. just so the thugs could assassinate her.
Remorse? Pretends to cry about Anna's death to allow Hans kill Elsa and makes excuses about it when the guards drag him to the boat, as it's even insisted দ্বারা the filmmakers themselves that at that point, nobody believed his lies anymore.
Basically, he is like Scar, commiting terrible crimes and shifting the blame purposely onto Elsa telling her to run away and never return. I like him though cause he does have some comedic moments which even they just point out how evil he is.