There is no way to answer this question without hearing the tone of voice used by both parties and the larger context in which the exchange occurred.
But its obviously that something deeper is going on here.
Person A didn’t list a preference either. Does that make person A rude as well?
That was my first thought too.
The way it works in my house is one of two ways:
Scenario 1:
Person A: Hey, Person B, I’m freezing and going to turn the heat up a bit.
Person B: Ok.
Scenario 2:
Person B: Why are you wearing three layers of clothing in the house? If you’re that cold - turn up the heat, dumbass. 
Person A: Ok.
The bolded statement is usually implied nonetheless. Life would be bland if we were always blunt about our answers…
In the same spirit, Person B could have helped the situation by the directly answering the question asked. Do you want to turn on the heat? “No.”
“Tonight’s not that cold” leaves open the possibility that it’s still cold enough to turn on heat.
It’s a sore subject with me. If people (and by people I mean the men that I’ve married) could just say what they mean and mean what they say things would all go a lot more smoothly.
Regarding the actual question posed in the OP though, no it wasn’t rude. Also not helpful, but that is not at all the same as rude.
But wait, if A&B have had a dozen (or more) conversations in which A has said “Hey, it would be a lot easier for me if when I directly ask you a yes or no question if you could answer with either a Yes or a No.” then I can see where A could argue that B was being rude. I don’t have enough information for a definite conclusion.
Why should it? Did anyone ask A for their opinion?
It is not inherently rude, or poor communication, to ask someone their opinion without prefacing the question with your own opinion.
My wife and I have something we call “Good Mystery and Bad Mystery”
Good Mystery - I wonder where we’ll be going out to dinner tonight
Bad Mystery - I wonder if he’s going to show up drunk again tonight
Sometimes bland is better.
Beats me. I think A and B are being equally non-committal (on the one hand last night was cold, and on the other hand today wasn’t as cold, so it’s a toss-up) and equally non-rude.
Of course. Although I would suggest that it’s a bit rude for person A to ask person B to choose something without letting B know in advance that A has a strong opinion on the issue. E.g. “Where do you want to go for supper?” “The Keg.” “I’m not in the mood for The Keg, I want to go to Asian Legend.” Not that that’s ever happened to me. 
My WAG is that Person B has a habit of dismissing, denying, and diminishing whatever Person A says. So Person A perceives “it’s not that cold out” as an invalidation of his/her previous comment in regard to feeling cold. This is a completely separate discussion from whether Person B is really rude.
This sort of thing is why I prefer to live alone. When I’m cold (or hot), I jack up the heat (or A/C). There is no discussion or debate, I don’t have to feel diminished or dismissed by the other person who is probably packing more body fat than I am, and I don’t need anyone else’s permission to crank up the heat. YMMV.
So you’re saying A is fat?.. It’s no wonder you live alone.
There may well be different communication styles at work.
My wife is a Southern lady, and she was raised with oblique communication: giving a straight “yes” or “no” answer to a question doesn’t come naturally to her, especially if there’s a chance that I (or whoever) might disagree with or even slightly dislike the answer.
I, on the other hand, often have trouble parsing oblique answers. I’m just not very good at it, for whatever reason.
So I often ask her, after she’s given an oblique answer, to give me a straight yes or no–or “either one’s fine.” I figure there’s nothing wrong with her communication style, so I can’t get mad at her; but if we’re to communicate successfully, I need to ask a clarifying question.
If I were A in the above situation, I might say, “Well, I’m cold; do you mind if I turn the heat on?”
No, I am not saying that.
What I’m saying is every time I’ve ever had a thermostat argument, the person who does not want me to turn up the heat has more body fat than I do* and does not feel as cold in general.
*This is not to suggest that *anyone *is fat because I have very little body fat, am poorly insulated, and get cold very easily. I also have Reynaud’s Syndrome, so if I’m a little bit cold, my hands go numb and turn funky colors and I can’t keep a grip on anything or work or type or do anything that requires fine motor skills.
Why doesn’t person A just turn the heat on?
Agreed that these are fairly similar cases. B is offering information, but not expressing a preference on the decision A is trying to make.
Now you’re just making it worse.
It’s not A’s fault that she has a slow metabolism and a thyroid problem. Now you’ve upset her and she’s going to eat that cold leftover pizza from last night and the pint of ice cream. Which will make her colder and she’ll turn up the heat and B will have to go sleep in the den with the window open but A will just think he’s avoiding her because she’s fat and they’ll get a divorce.
All because YOU are too skinny and you hate to live with fat people.
Nice.
Delivering a one-word answer would seem more rude, not less. Though it still wouldn’t be rude IMHO.
I saw what you did there. Hilarious.
Don’t you know there is no such thing as “too skinny”?
DTTLSSIDGF*
The correct answer for Person B would be to show concern for the comfort of Person A, not give a lackadaisical weather report.
The really, really smart answer would have been to take Person A’s hand, feel if the fingers were cold, and then say “Oh, my poor darling, you’re freezing! Of course you should turn up the heat!” Done correctly, this may result in an alternate suggestion.
Desperately trying to laugh silently so I don’t get fired.
If I got “tonight’s not that cold” or “I had chili for lunch” as a reply, I’d understand both to mean “no.”
I’m not sure why anyone wouldn’t unless they were autistic or just being obstinate. Or some kind of android with poor AI.
And OP, it sounds like you need a divorce.
Person A is overly sensitive and Person B should start working out and update his online dating profile. Life is too short to live with someone who gets worked up by non-events.