I'm also Jan 3rd and I love it! Never been at work or school for it I've had extra presents because people find stuff in the sales that they think I'd like in addition to what they'd already got! Hotels are cheap for a nice weekend away. Restaurants don't need to be booked. When I was little, my friends parents were pleased their kids had a party to go to at the end of the Christmas hols. I never had joint presents - my parents managed my birthday brilliantly and made it extra special just because it was so close to Christmas. The tree is always still up, which makes it feel holiday-ish.
DS1 is a fortnight after me and he also loves it - for the same reasons. Parties had to be indoors - but we knew in advance what the weather would be like! He's very academically talented. DS2 is early November and always enjoyed being older in the class, and having one of the first parties of each school year! He is very sporty, and clever but not academic at all. I think as boys they have been advantaged by being slightly older than a lot of their classmates.
My kids each had 2 best friends through primary school. Of both pairs, one had an August birthday and the other September. It was interesting for me to see the differences a whole year made, and definitely the August boys did not really catch up in maturity until Yr7, although one of them was an academic high flier.
Mid-winter babies do keep you warm! And an excuse to not host Christmas/New Year 🤣
I read some interesting research done with some European professional sportsmen which found that the majority were born Oct Nov Dec. There's all kinds of stuff about fetal nutrition at certain stages, and about when you progress to the next age bracket for your sport. In Europe that means that Oct/Nov babies might have a slight advantage physically. The school year structure in England means that autumn babies might have a slight advantage in terms of maturity, which might help them academically. Of course, in other parts of the world, the opposite will be true!
I didn't actively TTC, they were both 'unplanned' but wanted, but I had always said I'd prefer winter babies, based entirely on my own experience (my brother is May). And it's great! It's all about putting in the effort, as with most of parenting, and making the most of what you have.