So when the medieval folks would take a castle by escalade, the defenders had the option to simply push the ladders away from the wall. Question is, exactly how easy was this? This is assuming a simple ladder of adequate heft to accommodate a half dozen heavily armed and armored dudes going up a 30 ft. wall, and there’s several being deployed at the same time.
Also, is it safe to assume that the first one going up is screwed?
It would be quite difficult because the attackers would use a much more shallow angle than we use today. They could employ their forces to either dig holds for the base or manually brace it.
The optimum angle for a ladder today is much steeper because wh tend to use them on flat, hard, relatively smooth surfaces.
As a minor point, I question how heavily armored the average castle-storming dude would have been. Armor was expensive and heavy enough to make climbing a ladder challenging.
Castle storming is a rather hazardous occupation at best. First is consideration of the ladder itself, not the best in design or construction. Second would be the hazard of boiling oil, flights of arrows from corner turrets/towers, possibility of being pushed over or sideways to cause a fall.
Since we have more sophisicated defences and offences today we could have a separte discussion of modern warfare of a more practical nature.
In order to push the ladder the defenders would presumably have to expose themselves - if you have a bunch of archers at the base of the ladders you can nail the defenders while they’re pushing the ladder. You might lose a few men but eventually you’ll get through.
Unless you used long poles. 
And also because when we use ladders now, there’s not generally someone at the top trying to push it over ;).
But of course, the defenders would be using archers, too, as well as folks with swords or other melee weapons to try to kill the invaders as soon as they got off the ladders.
I saw a show on the history channel a while back (back when they were still doing mostly history shows) where they took a bunch of athletic guys and made authentic medieval armor for them. They then put the guys through a series of tests to see how they fared with respect to a lot of common myths. For example, there is a common myth that a knight in armor couldn’t get back up if he fell down because his armor was so heavy. They proved that this was just plain silly. Not only were the guys easily able to get back up, but they could run, jump over streams, run along the tops of walls, and do all sorts of things very easily.
The only problem the modern guys had was that they had gone from nothing to wearing very heavy armor overnight, and their joints hadn’t had time to strengthen and adjust for the weight. One of the guys ended up damaging a tendon in his knee just from the weight of the armor while doing these tests. If they had slowly trained and built up their tendons and ligaments and such they wouldn’t have had a problem.
Based on that. it seems pretty clear that a heavily armored knight could have gone up the ladder almost as easily as an unarmored man. If the heaviest knights wearing the heaviest armor could have done it, then the low level grunts with their cheaper and lighter armor wouldn’t have had a problem either.
It’s also worth noting that the knights with the fancy plate armor were the nobility. They were guys who started training with such armor at a pretty young age, so that by the time they were of “fighting age”, they were fully accustomed to wearing such armor.
Also, they probably weren’t going up the ladders, either. That was a job for the grunts in leather and mail armor, who would theoretically gain access to the inside of the fortress and open the front gate, at which point the heavily armored knights would be able to charge in on horseback.
Having made my own chainmail hauberk, I agree with the above. While the complete suit probably weighs 40+ lbs, the weight is evenly distributed over the entire body and really not that encumbering at all.
Plus, between ceramic armor, ammunition, helmets and canteens, it’s not as if modern infantrymen carry much less weight.
Can I refer the OP to those two well-known documentaries, Excalibur and The Two Towers? 
Just don’t stand or sit on the top rung of your scaling ladder, and maintain three points of contact with the ladder at all times or you’ll be subjected to OSHA fines.
A lot of times, too, those ladders aren’t set up like you would set up a ladder to paint the side of your house.
They would be carried up to the wall flat, over people’s heads, with a rider on the rear end of the ladder (sometimes). When the end nearest the wall was planted in the ground, the rider would be lifted up to the top of the wall, hopefully to start beating on defenders and secure the top of the ladder, thus clearing a place for newly swarming invaders to stand and begin fighting.
I never thought of that. To get a ladder to flip over, you’d have to push it past vertical, which would be tough if it was fully loaded and at a shallow angle. This would certainly make it easier.
Besides that, I wonder if rather then pushing it backwards it would be easier to have a couple of guys at the top grab one side of it and just roll it over.
Okay, you addressed the weight issue rather well. How about the cost issue?
Was it ever the case that medieval foot soldiers were extensively armored? I have a general notion that armor was mostly used on horseback - is that wrong?
Knights could also fight on foot if they had to. A horse isn’t much use during a siege, anyway, except as food.
Medieval foot soldiers varied quite a bit depending on the time and location. Sometimes they were just peasants who didn’t have armor and had to fight with whatever weapons they could scrounge up (like using the axe from their farm that they usually used to chop wood). Quite often though the grunts did have armor of some type. They couldn’t afford the fancy metalwork, but they did make armor out of other things. Sometimes they used padded leather, but one of the most common materials they used was just cloth. That might not seem like a good thing to make armor out of, but some heavy quilted cloth with a bunch of padding underneath is cheap and effective. It didn’t work as well as metal armor, but it did work.
Kawalski! Get over here!
To the extent that’s true, it’s mostly just because armor (at least, good armor) and horses were both expensive, so the warriors who could afford one could often afford the other, as well.