Greetings from Texas. Yeah, all that is true. You build based on how things usually are, or at least usually WERE when the dwelling was built.
I live in Houston -- very close to downtown, so I'm only about 50 miles from the Gulf of Mexico. This makes it VERY FUCKING WEIRD INDEED that my entire yard is covered in snow, and it is 16F outside. This is NOT Houston weather. It's almost unprecedented -- it's certainly never been anywhere NEARLY this cold in the 26 years I've lived here, and the idea that we really won't be above 32F (0C) for a material amount of time until SATURDAY is really really nuts. In a normal Houston winter, by contrast, we MIGHT see 3-4 nights that freeze. We go years without needing to wrap plants, and I've never bothered to wrap outside pipes before. (Outlying areas to the north and especially northwest of the urban core get as much as 10 degrees F colder, but even so it's not a regular thing.)
So yeah, we're all built here for cooling and not heating. Ambient air temp outside is rarely more than 95, so getting your house to 78 is pretty attainable. But when we get cold snaps, WE certainly notice in our house, which is a relatively new (1997) 3-story townhouse (very vertical; it's about 1800 sq. ft. or 167m^2). It's just not set up to heat evenly or well.
The first problem is just distribution. Our house has a modern 'open' style floorplan, with soaring ceilings in the middle (living) floor. Heat, of course, rises. The upshot is that if you set the thermostat to warm the lower 2 floors to, say, 65F, the 3rd floor main bedroom will be intolerably warm and dry.
As a consequence, a window in our bedroom is open about 2" all winter.
The other gotcha in our house is the floor in the first level, where I have my office (I work from home). It's a stained concrete floor, which is great in the summer because it helps keep the room nice and cool. Unfortunately, it does exactly the same thing in the winter. I'm wearing thick wool socks and long underwear in here now, even though I have a plug-in radiator to supplement the central heating.
Actually, the radiator -- a Delonghi; it works great -- would probably be enough IF the windows were better sealed. My desk is up against a window. My legs feel cold all day in weather like this (well, in cold weather; there hasn't been any weather LIKE THIS before), to the point that last week when it was much warmer (45F during the day) I was wearing sweatpants over jeans.
The house is wonderful and comfortable and attractive. It works GREAT for the vast majority of our weather. It just gets drafty in the winter. And, of course, today I'm concerned that we're going to get rolling outages. Whooo!
At least we have a fireplace. (People laugh about it, but in all honesty having a fire is the easiest way to make the living area comfy without overheating the top floor, just based on where the heat goes. If the house was a little bit bigger, I suspect it would've come with 2 climate control units and proper zoning, which would help a LOT, but as is: just one big zone.)