Using the SNAPSHOT Isolation Level will add a lot of load to the tempdb as your database load increases.
Changing the locking methods is best done via locking hints in the queries, or by changing the ISOLATION LEVEL in general for the stored procedure or connection. This is done with the SET ISOLATION LEVEL command, or by changing the isolation level on the connection object in .NET.
If you want SQL Server to handle its locking at a level other than the default page level (ie. row level locking) that has to be handled on a statement by statement level by using the WITH (ROWLOCK) hint within your statements.
UPDATE YourTable (WITH ROWLOCK)
SET Col2 = 3
WHERE Col1 = 'test'
There is no global setting to change this locking level, and if ROWLOCK is used in combination with the snapshot isolation level operations will still take place at the page level as the entire page has to be copied off to the tempdb database then updated then the old version has to be dropped from the tempdb database.