Although traditional dimension modeling – as explained by Ralph Kimball – tries to avoid snowflaking, it might help the processing of larger dimensions. For example, suppose you have a large customer dimension with over 10 million members. One attribute is the customer country. Realistically, there should only be a bit over 200 countries, maximum. When SSAS processes the dimension, it sends SELECT DISTINCT commands to SQL Server. Such a query on top of a large dimension might take some time. However, if you would snowflake (aka normalize) the country attribute into another dimension, the SELECT DISTINCT will run much faster. Here, you need to trade-off performance against the simplicity of your design.
There are several good tips here.