Ensure you have the necessary Snowflake account credentials and access permissions to read the data from the Snowflake database. This includes having a valid Snowflake username, password, account name, and the necessary role with read access to the tables you want to export.

Download and install SnowSQL, Snowflake's command-line client. It is available for Windows, macOS, and Linux. SnowSQL allows you to execute SQL queries against your Snowflake instance and export the results to local files. Follow the installation instructions specific to your operating system from the Snowflake documentation.

Configure SnowSQL by creating a configuration file (typically named `config` under the `.snowsql` directory in your home folder). This file should include your Snowflake account name, username, and default warehouse, database, and schema. This configuration simplifies executing commands by reducing the need to specify these details each time.

Open your terminal or command prompt and log in to Snowflake using SnowSQL. You can do this by running:
```
snowsql -a -u
```
You will be prompted to enter your password. Once logged in, you can execute SQL commands against your Snowflake instance.

Write and execute an SQL query to retrieve the data you want to export. For example:
```sql
SELECT * FROM my_table;
```
Use the `-o` option in SnowSQL to specify the output format, such as CSV, which is easier to convert to JSON later:
```
snowsql -q "SELECT * FROM my_table;" -o output_format=csv > my_table.csv
```

Use a local script or tool to convert the exported CSV file to JSON format. This can be done using Python, for example:
```python
import csv
import json

csv_file_path = 'my_table.csv'
json_file_path = 'my_table.json'

with open(csv_file_path, mode='r', encoding='utf-8') as csv_file:
csv_reader = csv.DictReader(csv_file)
data = [row for row in csv_reader]

with open(json_file_path, mode='w', encoding='utf-8') as json_file:
json.dump(data, json_file, indent=4)
```
This script reads the CSV file, converts each row to a dictionary, and then writes the list of dictionaries to a JSON file.

After conversion, check the JSON file to ensure the data has been correctly formatted and all records are present. Open the JSON file using any text editor or a JSON viewer tool to verify its structure and contents. This step ensures that the data integrity is maintained during the export and conversion process.

By following these steps, you can move data from Snowflake to a local JSON file without relying on third-party connectors or integrations.