Yes, regardless of the weather he'll probably have a great time
As he's so young be careful about how much you let him run about and don't walk too far or for too long. About 15 minutes is enough at 12 weeks, but you could carry him some of the time if you want to stay out longer.
He might find the sea a bit frightening and it's probably best not to let him go in, or at least no more than a paddle while safely on lead. My current Cockers have never taken to swimming in the sea and I'm very pleased about that because one of my previous Cockers used to like going in and swimming straight out to sea
. The first (and only) time he did that I really thought he was going to keep swimming away until he became exhausted and drowned but luckily he turned and came back, very tired, after a lot of calling from us. After that he had to stay on lead on beaches. Having said that, loads of people on here have Cockers who love to swim and retrieve or just swim close to shore and have a great time.
Don't let him drink seawater or eat dead fish etc. or you'll have a pup with an upset tum and make sure you have a towel and warm blanket for the journey home in case he gets wet and cold.
Apologies if this makes the beach sound like a place to be avoided
. It isn't and I love beach walks with my 2.