Drying depends on humidity. Unless you're heating your garage (accidentally or intentionally) that should be pretty much the same as outside, when the weatherstripped door is open. While it's raining, that's close to 100%, it won't dry. With the door closed and waste heat from the car and house raising the temperature, the water starts to dry. But that raises the humidity. Since the garage isn't really heated the humidity gets to 100% real soon, so drying stops. Even if it stops raining outside, on the inside that sealed door maintains a different micro-climate. Ventilate your garage better, and move the moisture out. How do you expect it to leave if you don't?
Once it's consistently below freezing, if the snow and snard lumps melt, it means you're losing house heat to the outside. A good thing only if that's how you want to make them disappear. Better you should slide them out on a shovel. And you'll still want ventilation to move the moist air onwards.