Is it possible to filter the list of databases in the Object Explorer of the SSMS?

This is now possible if you are using SQL Server Management Studio 2016. You can filter databases by Name, Owner and Creation Date.

I'm using SSMS build number 13.0.15900.1 - you can download a stand-alone version from Microsoft or just use this link: https://msdn.microsoft.com/en-us/library/mt238290.aspx