Does the order of columns in a columnstore index matter?

No, order does not matter. Each column is considered individually.

From the SQL Server team (emphasis added):

Typically you will want to put all the columns in your table into the columnstore index. It does not matter what order you list the columns because a columnstore index does not have a key like a B-tree index does. Internally, the data will be re-ordered automatically to get the best compression.

order doesn't matter, what does matter if that you should include ALL columns from the base table in the columnstore index - more via my previous answer to this question here

In SQL Server 2012-2016 you have the concept of Segment elimination (http://social.technet.microsoft.com/wiki/contents/articles/5651.understanding-segment-elimination.aspx) and you actually can force the order of at least 1 column (plus 1 extra inside each of the partition).

Consider the following article that explains data loading for better segment elimination: Data Loading for Better Segment Elimination