Alright, since no good answer has come up yet, I'll field this one.
There are a lot of misconceptions about wool, and they mostly stem from the horrible synthetic blends that parade around as "wool" in cheap suits, cheap coats, cheap socks, and cheap blankets. If your only personal experience with wool is with something like that, of course it seems like a horrifying material to wear, especially in a military uniform.
But wool was used for hundreds of years, if not thousands, because it was one of the most widely available, inexpensive, and versatile fabrics available to humanity until the last 40 years or so. Depending on the weave and thickness, wool could make quite comfortable blankets, coats, or cloaks, and was even used for athletic clothing and swimwear. Wool wicks moisture away from the body, making it an ideal fabric for cold weather wear, since the material will keep sweat from staying on the body and will prevent outer moisture from penetrating. Outdoor wear, even today, is highly dependent on wool as an inner layer, especially in socks, because other fabrics (like cotton) will swell with moisture and, once wet, will get extremely cold and make the outer layer essentially useless in preventing cold-weather fatigue and injuries.
Wool also stretches, and is extremely pliable and durable. Medieval hose, which were often meant to be skin-tight, were generally made of wool and were expected to last a year or more of continuous use. Heavier upper-body clothing, like doublets and coats and overcoats, et al, were often made from a heavier weave and were similarly durable and long-lasting.
So for military uniforms, wool is beneficial in cold climates because its moisture-wicking properties, and is also not as uncomfortable as you might imagine in hot climates. Wool breathes, it's part of the same microscopic geometry that makes it wick moisture, and so in even direct sunlight it does a good job of blocking sunlight while allowing fresh air to penetrate. An undershirt of cotton with an overshirt or blouse of wool was a standard of the US army, even in the west, where temperatures could fluctuate wildly.
So there's no reason that wool was holding anything back or was somehow sub-standard. Cotton blends became less expensive and as uniforms changed it was simply a better option for hard-use field uniforms, but wool remained the main component of dress uniforms for a very long time.
It's honeslty hard to find sources that argue all of this of any quality, partly because wool's ubiquity is itself a weird paradox; when it was the only choice no one wrote about it because it was obvious. Nowadays the assumption is that wool is terrible and scratchy and bad, thanks to synthetic blends. And now, of course, there are better options for many things. Performance fabrics and the like. Much of my familiarity with it is wearing wool uniforms at a working historic site, and just realizing that I was fairly comfortable even when the temperatures reached the 90s F, and when I changed back into modern t-shirt and shorts it made very little difference to my personal comfort.
tl;dr, though: wool is extremely versatile, and until the mid 20th century or so was abundant and inexpensive, and made an ideal choice for all sorts of uses.
. In the movies they got worse and worse imo.
