It happens a lot here in Canada since we have long and cold winters.
I tend to use a plastic card from my wallet .
It can bend to the shape of the window which is concave inside.
It's not very fast and it's pretty annoying
but when you are in a hurry it's better than heating the car and waiting for it to melt.
I suggest using a card you don't use often instead of a credit or debit card because sometime the card can snap or bend and the magnet stripe might be damaged.
lifehacks.stackexchange.com/users/24432/Berchy
If you have excessive condensation inside the car you need to dehumidify your car interior...
You can use those dehumidifying boxes with silica gel crystals or I have seen a suggestion of using kitty-litter gel crystals knotted inside an old sock and sticking it on your back shelf or dashboard.
I presume the dampness arises from wet passengers dripping water on the carpet/upholstery rather than a leak.
You could try sticking the heater on full blast with the windows slightly open to dry it out on a long journey.
My car has an electrically heated rear window so its less of a problem for me.
On previous cars I have used an ice scraper on the inside, but they work less well as the curvature is "wrong" - concave rather than convex.
lifehacks.stackexchange.com/users/2233/Dave45
Take the largest container of the hottest water you can carry.
If the water from your tap doesn't get very hot, consider turning up the max temperature on your hot water heater temporarily.
Otherwise, boiling it on the stove might be your better option.
Take this container and slowly pour the water over your car window, being careful not to get any on yourself of course.
The heat from the water will transfer to the window, melting the ice that's formed on the inside.
Alternatively... Take a hand warmer, or a microwaved rag, and wipe the ice away with it.
The heat will melt away the ice.
lifehacks.stackexchange.com/users/8/GimmeTehRepz
I had this issue with my 2006 Tundra and its sunroof.
The sunroof sealing system is designed with passive drainage and the weep holes can get plugged up, which allows water to overflow/seep inside the cab.
Use an air hose to blow out weep/drain holes in corners when sunroof is in open position.
Also, close heater vents to "recirculate" option when weather is both sunny (warm) and rainy/cold, which can cause a condensation situation.
The recirculate setting shuts down the outside airflow into the cab.
lifehacks.stackexchange.com/users/18265/jkraft
If you have frozen water built up on the inside of your car windows, while keeping your heat on, you can run your air conditioner with the setting that lets fresh air come in.
The AC will help dry out the air on the inside of the vehicle and prevent it from fogging up and freezing.
lifehacks.stackexchange.com/users/1505/Jason Hutchinson
With my precious golf3 I had the same problem, the moist was creeping in and staying there; even though it got away for day or two after driving for hours with AC set on hot (not too pleasant btw.)
it kept getting moist all over again.
Doing something against this may mean replacing the rubber sealings of your doors or similar, but maybe it is just a one time thing for you, in this case one of the things I tried was: Put some bricks into the oven, set to highest temperature, and leave it there for quite a while.
Then quickly put them into some container that withstands the temperature (steel bucket in my case) and put it into the trunk of the car.
Removing anything that blocks the air flow (hat shelf, flip over the rear seats if you can).
Start car, set AC to really hot, and do not completely close the trunk (just so much that you could stick a scredriver through the gap).
If you get the amount of bricks right, it will quickly heat up the back of the car, causing most moist to evaporate.
Hot dehumidified air from the AC will enter at the front and leave at the back, drying out the car pretty well.
The number of bricks depend on your ovens temperature and your cars size.
Do not use too many or you might seriously damage something (a lot of stuff in a car doesn't like anything more than 50°C)
lifehacks.stackexchange.com/users/1473/PlasmaHH
You may need to give the inside of your windows a good clean.
Condensation tends to form around the small particles of dirt on the screen.
If you are prone to wiping away condensation with a cloth/sleeve etc.
, you'll be making the problem worse and worse.
In cold weather, this condensed water will freeze.
So prevention may be better than a cure.
Give your windows a good clean and polish and hopefully this problem will occur less often.
lifehacks.stackexchange.com/users/2184/Duncan Jones
I was thinking of using a hairdryer (like the handheld electrical ones) to just warm up and blow the water away.
However, the water might drip into the car.
lifehacks.stackexchange.com/users/24450/Trajan Espelien
So being so cold as it is. My car doesn't see the sunlight, and therefore there is condensation forming on the inside of the windshields. I could get most of the ice out by placing the heater direction towards it , but that still leaves the back windows that are almost untouched and ice formed.

Is there another way to remove ice from the inside if the sun doesn't shine on it?
How to remove ice formation inside the car windows
lifehacks.stackexchange.com
<winter><car>
lifehacks.stackexchange.com/questions/3749
lifehacks.stackexchange.com/users/2118/JeffJeffery
There are a number of ways to remove ice formation from inside car windows, and a common method is to use a plastic card from your wallet. You could also consider pouring boiling water over the windows of your car or use a microwaved rag to wipe the ice away. Alternatively, you could just put your AC on very hot or use a hairdryer. The options are to scrape the ice off using a credit card or plastic scraper, dehumidify the car with silica or cat litter, pour very hot water over the windows, unblock drainage holes, set the heater to 'recirculate', place hot bricks in the trunk and run the heater in non-recirculating mode, give the windows a good clear, blow the water away with a hair dryer.
Scrape the ice off using a credit card. Dehumidify the car using silica gel or car litter. Pour a lot of very hot water over the car windows or wipe with a rag heated in a microwave oven. Use an air hose to blow out potentially clogged weep/drain holes and set the heater vents to 'recirculate' to avoid introducing damp air from outside the vehicle. Run the car heater with air coming in from the outside to melt the ice and dry the car. Try replacing the rubber sealings on the doors or heat up bricks in an oven and place in the trunk in a suitable container and run the car heater to dry it out. Give the windows a good clean. Try using a hair dryer to blow the water away.