What are those Wooden Tube thing?
Yes their purpose is to store water or a different liquid.
I've seen them in other anime and manga but I cannot remember them though.
 In general they've been used all around Asia.
This one for example is from Borneo and it can be seen that it is heavily decorated:


Here is the Shop were it is available more information.

It has current day versions like these:



link



link


link

They are usually handmade, being made in the wild when hiking or camping like this.

This is all the information I could gather including some japanese websites (I have no knowdeledge of the Japanese language). I found information only on shopping websites and I hope it is not against the rules. I hope it is a conclusive answer even if it has ambiguous sources.