We are planning to visit Zugspitze peak late June and read in TA that it can be cold at the top like 6degC even in Aug. Do we need to have thick jacket when up there ?
It will be a lot colder on top for sure (includes three glaciers). Dress in layers rather than carrying a big winter coat. If you get too cold you can retreat to the restaurant to warm up and enjoy the views.
It won't feel all that cold should the sunshine that day. If the wind isn't too strong you can walk around in a t-shirt up there. The wind can be nasty and chilly, though, so one should definitely bring a windbreaker or other light jacket. With a couple layers - shirt + sweater + light jacket - you'd be well prepared.
It is kinda a differend cold. I call it a dry cold in the mountains and feels rather pleasant. But you are high up, so jacket for sure that you can take off. It will feel rather warm if the sun comes out, but it will not be beach warm