Beachcombing can be done any time of the year. The winter might be an interesting time because there are less people and more opportunities to find interesting things.
Both Summer and Winter have their perks. However, I would avoid beachcombing during hurricane/monsoon season. Although storms can be beautiful there are many degrees with beachcombing at this time of year.
It depends on what beach you're on! If you're looking for population intense beaches, then often the winter is the best time. In the summer it is often hot, but if you look to the north the beaches are often busy.
Well these are some personal preferences. Personally I prefer the summer; you can stroll with your sunglasses, goggles and other specialties for summer beach combing.
