elly, I think your Dec 3 date sounds fine. That would mean close-by friends would get them on the 4th and out-of-state friends on the 5th. I wouldn't think it was early. Every year we get our first card (and only that one) on the first mail day of Dec exactly, from the same friend. She is outrageously organized. Every year she mails her card, family photo and long Christmas letter promptly on the last mail date of Nov and she puts everything related to that chore away before it's time to change her calendars to December. It's very important to her. Every year I get a "too early" feeling from it (not a bad feeling, though). Usually hers is the only one for a day or 2, then they start arriving. I would rather be the person who has my card sent to a friend somewhat early, but I'd like them to at least be used to the idea that it's December.
This makes me consider the opposite - that I really don't think any date before Christmas is "too late". Since I plan long and hard for finding meaningful cards, and try to make it a family experience for dd, I would like to think they arrive at friend's homes early enough to be a part of any decorating they may do. And that they don't arrive so late as to maybe be lost in the shuffle of that household's frantic moments. But if I got the cards into my friends homes on Christmas Eve, I would still call that a "win"!
Here's another thought or memory jogger - is there anyone on your list to whom you also send a birthday card during the season? HRH's brother's bday is right in the middle of Christmas Card arrivals. I try to make his birthday card separate and special, and send their Christmas card at least a few days apart from it. This is a time when I will definitely use a "Happy Birthday" seal/sticker and won't use a Christmas stamp or Christmas return address label, because I want him to see his birthday is as unique a day to us as anyone else's through the year.