Asking questions about flawed logic is firmly within the domain of the philosopy of logic. Arguments and conclusions drawn from them which seem logical, but are actually not are commonly known as fallacies.
What exactly is a fallacy? Well, that depends on one's theory of fallacy, and there are differences in perspective among serious students of philosophy of logic and fallacy. But, there are three generally accepted criteria for identifying an argument as fallacious, specious, an act of sophistry, etc.
- A fallacy must be a 'bad' inference, and inference by nature requires premises and conclusions. Many people confuse a false fact for a fallacy and often laypersons use the term fallacy for describing both poor reasoning and a poor proposition. MW's entry 'fallacy', in fact, has several definitions. But among philosphers, the definition is constrained by convention to arguments. Different theorists have slightly different views on what is the right way to conduct inference. Two major classifications of fallacies are formal and informal fallacies, where the former is a question of syntax or the symbolic form of the argument and the latter is a question of semantics, or the meaning of symbols.
- A fallacy must be 'persuasive'. One can, after all, assemble a ridiculous argument that would fool no one. Those in the business of understanding fallacy prefer not to waste their time on absurdity.
- And generally, there are criteria of what constitutes 'good' inference. Different theorists have different statements of necessary and sufficient conditions, however, according to T. Edward Damer in his Attacking Faulty Reasoning, those criteria are acceptable, relevant, and well-grounded claims.
Since 'good', 'bad', and 'persuasive' are open to interpretation, these criteria admit quite a number of theories.
Let's now examine your example to demonstrate the former principles. We will use a simple syllogism for clarity. In natural language use, the most important skill is determining synonymy between expressions. This can be a messy process, which is why many philosophers who delve deeply into the bowels of mathematical logic prefer formal fallacies. But let's have at it anyway:
P1. The weather is currently a cold spell.
P2. (Global warming means weather should be getting warmer.)
C. Therefore, global cooling is true.
Perhaps the most famous politician in the US Congress for arguing along these lines is James Inhofe who made national news by throwing a snowball on the Senate floor to deny global warming.
(On a personal note, such poor reasoning from members of the most powerful deliberative body in the world is disconcerting.)
So, let's look. P1 is clearly a simplified claim to match the idea that a "freak snowstorm" may represent a single event which is confuzzled with a trend of being a cold. Of course, it would be a fallacy to cherry pick one event and try to foist it as representative of a series of events. P2 isn't explicitly stated in your example. This is called an implicit premise, and give the nature of the deep structure of a language, can be a contentious act in and of itself. Lastly, the conclusion is drawn! Of course, it's a bad conclusion.
Overall, the argument appears to be a conflation confusing weather with climate. The former is the current state during a moment of time and the latter is a general trend over a period of time. Certainly, a snowstorm (weather) plays a role in determining the measurement of climate. But global warming says that there's a mathematical gain in the arithmetic mean of the global temperature predicated upon statistical trends arising from tools such as principal component analysis (PCA). It does not say that every day it's going to be hotter than the last in a specific place. (Convection currents in the atmosphere are quite a complicated phenomenon.) But ask a climate change denier what he believes are the flaws in the use of PCA on record reconstruction of tree rings, and you're not likely to get an adequate response.
An interesting and relevant notion to the study of fallacy is an underlying difference in epistemic methods between experts and laypersons, and how people deal with the epistemological source of knowledge 'testimony'. There is much discussion over the philosophical term 'folk psychology' about what constitutes how ordinary people go about evaluating the thinking of others, including experts. Combined with the psychological idea of the Dunning-Kruger effect where science has demonstrated that some people build poor models of their own ability to reason, it's easy to understand why someone who was raised in an anti-intellectual, anti-government environment might manifest such poor reasoning about global warming which is generally an object of study by government-funded, climatologists with PhDs who hail from elite academic institutions.
Anyway, anywhere you find an argument that seems logical, but isn't, you're dealing with the notion of fallacy.