Hardly. People of that era didn't have the mechanical systems available to allow them to ignore their environments like we do today. As a result, their designs themselves had to do it. This can be seen as you look at traditional architecture all over the world. That's true whether we're looking at the Greek Isles, Japan, or Ethiopia. This effect can even be seen as you look at single styles of architecture. Italian Renaissance is different from French Renaissance is different from Polish Renaissance. Why are they different? Because each region adapted the style to their unique environmental conditions. The French buildings have steeper roofs than the Italian buildings because they have to deal with snow. The Polish buildings often have taller windows because daylighting is a bigger concern there.
There is certainly a cultural influence on the building designs, but I don't know of any culture that did not adapt their styles for their environment. Provided they've been there long enough to adapt.
Oh, and monumental architecture like palaces, shrines and temples don't count.
The Nords have been in Skyrim for thousands of years. That's more than enough time to adapt. Yet their architecture shows no sign of adaptation whatsoever.
You're basically saying the sciences behind art history, archaeology, and anthropology are hogwash? I'm not sure what you're trying to argue or disagree with at this point...
Are you saying that French buildings are different from Italian buildings because of the materials they used, but not because of the differences in culture? Correct me if I'm wrong, but that's just silly. Do I even need to rebut that? It takes care of my counter-argument for me. They're different because the cultures behind them are different. French is not Italian. Period.
You would have more success arguing the difference between Italian and Sicilian styles, but even then, there are plenty of similarities due to the two groups sharing cultural similarities.
Example: I can point to a French building and tell you where and from what cultures the various motifs, architectural elements, and artistic styles are from. The Renaissance, being an artistic and intellectual movement that was a throwback to the classical eras, featured a return of the rounded arch--a uniquely Roman architectural feature. Are you saying that because the Romans built them out of stone, a wooden round arch is not a Roman architectural style? So while the building might be made by the French, in France, the use of a rounded arch is a uniquely-Roman (and therefore Italian) style.
Columns and the orders of design behind them: You have Doric, Ionian, and Corinthian for the Greeks. The Romans borrowed these, and added their own: Etruscan and Composite, among others. Because of this, I know that if a temple (or house since you're averse to structures that disprove your argument) uses Doric-order columns, it is likely Greek. But I also know that if the temple is arranged to only have stairs in the front (not in the round), it is either Etruscan or Roman. If those same Doric columns are made of wood, there's a chance the building is Etruscan. The point is, I can tell you something about the style and where it came from.
Applied to the game, I can tell you that Falkreath is a Nordic city because it shares the same features of the buildings in Whiterun and Winterhold. I can tell you that Bleak Falls Barrow is a Nordic ruin and not a Dwemer ruin (despite them both being built NEXT to each other and from the same materials) because the style is different.
[EDIT - Sure they've adapted over time and environment. I've already given examples of in-game ancient history as compared to the modern period. I'll take it a step further: Looking at Caesar's palace in Vegas (or even the Paris), you can tell it's supposed to be Roman. Just because it has a skyscraqer, is built with steel, has central air and heating, and a very nice pool doesn't make it a different style--or belonging to a different culture. You could argue it's a modern Roman inn. =) ]
Look, I don't want to drag this topic off-topic. I presented a sound art historical and anthropological argument to offer an explanation to the OP as to why the cities might look similar. I'm sorry you want to debate the very nature of art history with me, but in the interest of keeping the thread open, I'm going to leave my arguments thus.