The short answer to this is yes, "technically" it's possible to put a litter box on a balcony in winter, but it's not at all realistic and will not work out in any way. You can, after all, put anything that physically fits on a balcony.
Addressing the issues in no particular order, we'll start with weather. The cat will need to access it, not only in the cold temperatures you're asking about, but in hot weather, humid weather, wet weather, windy weather, any conditions you may encounter. That doesn't mean the cat will want to access it, however. If it's raining, if the litter box is buried under several inches of snow, if it's overly windy or overly hot, you're far more likely to find the cat has availed itself of your laundry basket, rug, or bed instead of going out in lousy weather. Similarly, if it snows, the litter box is now buried. If it rains, the litter box is now either a waterlogged mess, one large clump, or some combination of both. Plus, with the open door, you're probably still going to be able to smell it.
You'll have safety concerns. Again, you're going to have to leave the door open; I expect you aren't living in a situation where a cat flap can be installed in the door, so the door itself needs to be left open, leaving you with an unsecured apartment. You'll also have a risk of the cat being injured, either by falling if the balcony is at a dangerous height, or by traffic below if it lands safely. Even if the cat departs the balcony for outside with no injury, it's very unlikely now that it will be capable of returning to it, and will be subject to all the risks of harm that affect any outdoor cat. (Additionally, you may be in violation of adoption contracts, depending on the terms set out by the rescue agency.)
You aren't avoiding anything; regardless of whether the cat uses the litter box or your pillow, you're still going to have to clean it up. An outdoor box is not going to magically clean itself, and with it being "out of sight and out of mind," it's likely to be much dirtier than a box kept inside and regularly cleaned; with frequent cleaning and a good quality litter, there's minimal odor associated with a properly tended litter box. If you dislike the idea of cleaning up a few clumps once a day so much that you're trying to find some way around it, either get a self-cleaning litter box, or get a fish.
Your neighbors will hate you. They'll also be able to smell it if they open their windows. Any time the wind kicks up, it'll blow dirty litter at them. If it rains hard enough to overflow the box, it'll ooze out onto both your balcony and anything that it can drip through to (and you are the one responsible for cleaning that mess, as well). If the cat kicks litter up, it'll land on the balcony below. You'll be forcing neighbors to deal with your mess.
If you want to adopt a pet, that means accepting all parts of adopting that pet, including dealing with proper disposal of its waste. If you're unwilling to responsibly clean up after your pet, then you absolutely should not adopt a pet at all; if you express your disgust with cleaning up after it to a rescue, it's likely they won't approve you for adoption, as you would be giving a red flag that you would not be a responsible pet owner.
