Bourbon and Dice
Before anyone brings it up (though you are still welcome to if you want, of course), I have heard arguments that sleeping in armor isn't all that uncomfortable. But even still, I've decided that in my world it would be. It presents some interesting choices for the characters about whether they will risk trying to sleep in armor, or sleep without it but risk fighting in the middle of the night with a lower AC.
I won't go into the realism of it either, but have you considered that you are making Dex even more of the ultra stat by doing this? Knowing that they'll be likely to go without armor more players will be inclined to use dex than heavy armor.
Ah. It's interesting to me that some people really dislike the idea of sleeping in armor being a difficulty. Not that you're wrong for disliking it, just that the idea has never bothered me, but it bothers some people.
Part of my motivation for the rule is that I wanted to make certain items like tents and sleeping pads more meaningful, as well as making the survival check a bit more meaningful (i.e., with a successful check, you can make a natural shelter that protects you from the elements just as well as a tent would). If everyone sleeps just fine in the wilderness, then who ever needs a tent or sleeping pad? Another part of my motivation was to give players an interesting decision: Do I sleep with armor on and chance it, or sleep without armor and chance that we won't be attacked? The fights in the middle of the night where the paladin or fighter have to get up and fight in their skivvies with a lower AC sound kind of fun with the extra challenge.
Those fights can be fun for the first few times. But eventually your players will get frustrated by "another night encounter where I can't use my armor."
Making tents and sleeping bags and bedrolls more useful is something I can get behind. I like having all of the necessities on my character. Of course, I'm a huge fan of Aurora's Whole Realms Catalogue too.
Something you may want to consider for cold weather is the amount of activity that someone is performing. I recall a fable where two people are climbing the trail up a mountain in the biting cold of winter. They come accross a man who is injured and can't walk. One of the two travelers leaves him behind because he is concerned that he'll get slowed down and won't make it before he freezes. The other picks the man up and carries him. Once near the top the 2nd traveler comes across the frozen body of the first. Turns out the extra body heat from the exertion of carrying the injured man helped keep him warm while the other guy succumbed to the cold.
There was a culture of nordic style sorcerers in the 3e Scarred Lands campaign setting that when they casted spells it generated body heat so they could run around the frozen north with almost nothing on