I've got 2 winter, 1 summer and 1 autumn child and there are pros and cons to all.
Winter:
Pro: in the older half of the school year which is good for confidence
Con: shit time to have a birthday imo. I have a winter birthday and hate it. Personally I took steps as far as possible to avoid a December birthday. Restaurants and party venues will always be booked up with Christmas parties for most of December, and if it's too close to Christmas I think you lose some of your special day.
Summer:
Pro: lovely time to have a birthday - think BBQs, outdoor parties, outdoor events for the rest of your life, not just childhood. Late July and all August birthday children don't have to go to school on their birthdays.
Cons: in the U.K., one of the youngest in the school year. Although this isn't necessarily a disadvantage.
Also, you can apply to start school a year later for summer borne children if you feel it is appropriate. Hay fever season if you're prone to it. June birthdays might clash with exams.
autumn:
Pro: oldest in the school year. Autumn born children tend to get picked for sports teams more being older and bigger. Being one of the older ones can help self confidence.
September usually still warm so still lots of outdoor possibilities for activities / parties/ trips away etc without the crowds of summer. October and November can be beautiful with the changing leaf colours.
Cons: November is almost winter - it's cold and dark. The school year groupings in the U.K. are set in stone for autumn and winter born children so if you have a very able child, they will in a sense, be held back, as unlike summer born children who can be moved down a year if thought appropriate, autumn borns cannot be moved up a year.
Personally, I'd go for summer based on my experiences alone.