Is it possible to set DEFAULT TRANSACTION ISOLATION for all connections in SQL Server?
It is not possible to configure Snapshot Isolation (SI) as the default isolation level.

To use SI, the database must be enabled for Snapshot Isolation:

ALTER DATABASE CURRENT
SET ALLOW_SNAPSHOT_ISOLATION ON;


Then each connection must explicitly request SI, using for example:

SET TRANSACTION ISOLATION LEVEL SNAPSHOT;


It is possible to set the default Read Committed isolation level to use row versioning (RCSI).

If Read Committed Snapshot Isolation (RCSI) is sufficient for your purposes, the setting is:

ALTER DATABASE CURRENT
SET READ_COMMITTED_SNAPSHOT ON; 


Further reading:


Snapshot Isolation in SQL Server (documentation)
How to set the default transaction isolation level server wide? by Nacho Alonso Portillo