How can you insert data into a ARRAY column on a Snowflake table using SQL?
It looks like you need to apply a function to parse the array. As of 9/13/2018 functions are not allowed in value lists see Is there a literal syntax for arrays

One way around this is to combine INSERT INTO and SELECT statement. Example:

CREATE OR REPLACE TABLE array_test_table (
  id number,
  ids array
);

INSERT INTO array_test_table (id, ids) 
SELECT $1, PARSE_JSON($2)
  FROM VALUES (1, '[1,2,3]' );