Been riding around during the day without the doors this past week (minus the rainy days). Just rocking a heavy sweatshirt and gloves, I love the looks I get in the morning driving to the gym in about 40*F weather
As for the mirros, I've heard as long as there is A mirror so you can see behind you (aka rearview), you're ok. I'm not expert, only had my Jeep since Feb, but had the doors off for 75% of the summer. I'm in the greater Boston area, so I'd assume a Jeep with no doors would stick out to the cops around here, but never had an issue.