I load mine the night before, leave it the house, take it out in my soft case in the morning(law to have gun encased before legal hunting hours) and then take it out go hunting. I leave my soft case unzipped and open in the truck, after hunt into the case and into the house. I will let it climatize slowly in the case then take it out and store open muzzle down. Never had any rust or problems with this method. Personally leaving it the truck here with dew or frost I am not sure it would be a beneifit, not to mention the drive out in a warm cab. I have always found warm to cold leaves little mositure but vice versa it become evident.

If wet I tape my muzzle with electrical tape and in heavy moisture will seal the breech as mentioned. Also following the hunt in these condition I have took no chance and dumped the load and cleaned. Even if going the next morning. In dry conditions I have left it loaded for weeks with no effects on shooting or rust signs.
I don't use any bore butter, etc, just clean with hot water or at the range a windex/water. Follow up with alcohol, dry patches and when store coat the barrel with good quality gun oil. Remeber to remove before shooting to ensure pressure is not to high!

If this method is incorrect I have yet to see any effects in a number of years be it rust, pitting or accuracy loss.