Does your air conditioner work? I'm guessing not because it took so long to clear the windows. The a/c also dehumidifies the air when the defroster is on.
You did indeed feel the tires leave the ground in those puddles, hydroplaning it's called. It happens when the tires ability to displace the water is exceeded, slow until grip is restored.
Anyplace that requires chains is no place for summer tires, with or without the chains. Take the Honda where you'll have a way bigger cabin to fog up.