Hi Raelgrin,
I keep a clean dry hand towel in the car and I use that in the mornings to wipe the inside of the windscreen. That removes almost all the moisture - enough to drive the car straight away - and setting the heater to demist to blow on the windscreen then keeps it clear.
It's a good idea to keep several old hand towels for the car - drying after washing, cleaning the windows and windscreen etc. You can keep them clean by just throwing them in with other towels whenever you do a wash. Hope that helps.