Answer from a person who spent quite a lot of time inside armours, reading about armours, and helping to excavate and document several, so I can tell you where are the holes in entire problem

:
1. Meh, it's easy. Pretty much the same you pee without the armour, when it's cold

Most of the time crotch is easy to get to. First of all, pants looked different in medieval. Until late XIV c. it was two separate legs attached to belt over underpants (a suspender if you will

); then, when the upper wear was shorter - they made it into one piece of clothing, with a hatch in front. Plate legs used same design and didn't cover crotch. When in chainmail, well that's trickier, but it also has to be suspended in several places, so no big deal.
Aiming for a crotch in battle is so hard and so inefficient, that even if the knight is on foot, there really is no sense in doing it, hence it being so exposed was hardly ever a problem.
Number two on the other hand... Man, it's hard to s

t in armour. You have to hold the chainmail or else it gets in the way (lots and lots of small circles), and if you do it in woods - you also have to hold on to something. Because of the plate legs, it's hard ro roll the underpants down as well. It's a horror. Still beats what ladies in long gowns have to deal with, though.
2.
Padding *. Why do people always forget about padding. Due to simple physics of energy distribution, putting a full plate or mail on yourself doesn't really do anything, you need padding underneath it. Said padding, after 40 minutes of fighting (and note, that battles in medieval usually took at least several hours) is
soaking with your sweat. That's your problem with rust, not half a pint of pee

The problem is bad on autumn and spring, it's a hubris in summer. It wouldn't be so bad on winter, but it was unusual and expensive to wage war when it was cold (no pasture for horses, hard to manoeuvre, and metal tends to sunder
very easily (and the stuff armours was made of especially, as it had a LOT of carbon.)
3. Knights fought from their mounts. That was their thing, that was why they were so armoured. Sprinting 200m in full plate and then standing on your hands is easier than you'd think, the weight of full plate is lower than what commandos have to carry around for their 14 miles runs. But it was goddamn expensive, and special, privilege-wise.
THIS is where the pee problem lies. Ever peed from a horse? Before the battle (so when the knight would actually wear his armour) they stood ground, usually where the terrain favoured given side. And it was impossible to go for a quick one in the lue thanks to groups of lightly armoured knights from both armies who were riding as close as possible to enemy lines to lure them out (dunno the english word, "podjazd" in polish).
How they dealt with this problem? Same way snipers do nowadays
* Damn wikipedia, man. Gambeson, aketon and padded jack are three very different kinds of padded armour, not synonyms :|