Пост в Ust-Kamenogorsk, East Kazakhstan, Kazakhstan

There are no problems with the entrance to the Altaic Alps. In winter at any time you can come there. It's a ski resort, snowboard, skis, rooms and cafes.)))

You can get a permit by a travel agency. But obviously that costs money. Also there are some non restricted areas, you can visit without permit.

What kind of permission are you all talking about? I hear that first time. If you go to Kazakhstan you need to be registered by host in a local police during 5 days upon arrival, otherwise you could have a problem with immigration police. If you want to go hiking there is no need to get any permissions. Though there are some restricted areas in the mountains those are regulated as national parks you cannot go without special permission.