Sounds like a combination of cold weather and short journeys;car never gets to dry out.A/C won't be operating at low temps. anyway.

Try cleaning the inside of the screen thoroughly with ordinary household window cleaner. Best time to do this is when the thing's nice and warm after the car's been used a bit. I find that a clean screen is far less likely to form condensation and thus ice on the inside.

I have always found that a condensation / icing problem usually disappears after a good clean until the dirt film builds up again. Also running the airco with the heater once the vehicle is warmed up will dry the air in the car, making condensation less likely when it cools overnight. Most climate control systems do this anyway to maintain humidity levels, so if it has such you shouldn't need to do anything here.

I also have an i20 with a similar problem. Its on a 59 plate and I have regularly had to scrape ice from the inside of the windscreen. When its not quite as cold I have to clear condensation from both the front and rear windscreen that the blowers just can't clear. My car has been back to the garage it came from quite a few times and from what they've told me Hyundai UK know there's an issue but are unable or unwilling to fix it so are ignoring it.

Mine's that bad that I'm considering taking legal action as as far as I'm concerned (and the dealership agree's) the car is just not fit for purpose. I've also had i20 courtesy cars from the garage with exactly the same problem. Be interesting to know how many people are also having this problem.