Thank you, folks, for all the good replies and suggestions you've been sending. Some I've already tried, some are new and are worth trying. (I really like the school chalk one!)
I realized, just after I'd posted the question, that I'd forgotten to say what the car is. It's a 2007 Kia Rondo, which is a crossover model, and the color is dark blue.
The carpet is soaking wet from all the snow. Yes, Ann Arbor gets very cold in winter. There's been a fair amount of snow (though nothing like what so many of you everywhere else have been getting whacked with this year). But it's like this every winter, and I haven't had this problem before.
I usually have the heater all the way up and the fan on high when I'm driving. When the inside has been frosted, I've been doing as suggested, with the defroster setting on and the heat and fan both set at high. This still takes a good 5 or 10 minutes or longer for the frost to be gone, depending on how frosted up it is.
I took it to the dealer on Friday to ask about this. The service guy mentioned the climate control setting, which I'd always had off because I didn't really know how it worked. He said have it open while you're driving but close it before shutting off the engine. I did thate, and there was no frost this morning. None outside, either. (For that matter, what causes frost to form on the outside some cold nights and not others?)
Yes, the curvature of the window is the same inside and out, but outside it's convex (so the middle of the scraper blade gets it), while inside it's concave and only the very edges of the scraper get it.
I will definitely try out running the AC tomorrow and also cracking the window a bit. Thank you!
My driving is almost all short trips, and my driving patterns have not changed.
I blame the weather, too. (I HATE winter, grrrrr.)
That sounds like the best idea yet, to check out frost on the outside of a beer mug to see how my windshield frost compares.
Thank you, everyone!