Begin by exporting your data from Todoist. Todoist allows users to export their project data in JSON format. Navigate to the Todoist web app, go to the Settings, and find the "Backups" section. Download the latest backup file, which is typically in JSON format.

Set up your local environment to handle the JSON file. Ensure that you have Python installed on your machine, as it will be used to parse and format the data. Install necessary Python libraries such as `pandas` and `json` using pip:
```bash
pip install pandas json
```

Use a Python script to read the JSON file and transform it into a CSV format suitable for Snowflake. Create a Python script that reads the JSON file, parses it, and converts it into a structured CSV file using pandas:
```python
import json
import pandas as pd

with open('todoist_backup.json', 'r') as file:
data = json.load(file)

# Assuming data is a list of dictionaries
df = pd.json_normalize(data['projects']) # Adjust path according to JSON structure
df.to_csv('todoist_data.csv', index=False)
```

Upload the CSV file to a cloud storage service that Snowflake can access, such as Amazon S3, Google Cloud Storage, or Azure Blob Storage. For this example, we will use Amazon S3. Use the AWS CLI to upload the file:
```bash
aws s3 cp todoist_data.csv s3://your-bucket-name/
```

Log in to your Snowflake account and create a stage that links to your cloud storage. This stage acts as a reference point for Snowflake to access files stored externally. Execute the following SQL command in Snowflake:
```sql
CREATE STAGE my_todoist_stage
URL='s3://your-bucket-name/'
STORAGE_INTEGRATION = your_storage_integration_name; -- Ensure you have set up appropriate storage integration
```

Create a table in Snowflake that matches the structure of your CSV file. Use the Snowflake `COPY INTO` command to load the data from your CSV file into this table:
```sql
CREATE OR REPLACE TABLE todoist_data (
project_id STRING,
project_name STRING,
... -- Add other relevant columns based on CSV structure
);

COPY INTO todoist_data
FROM @my_todoist_stage/todoist_data.csv
FILE_FORMAT = (TYPE = 'CSV' FIELD_OPTIONALLY_ENCLOSED_BY = '"' SKIP_HEADER = 1);
```

After loading the data, perform a series of checks to ensure the data integrity and accuracy. Use SQL queries to check for any missing or incorrect data entries. For example:
```sql
SELECT COUNT(*) FROM todoist_data;
SELECT * FROM todoist_data WHERE project_id IS NULL OR project_name IS NULL;
```

By following these steps, you can successfully migrate data from Todoist to Snowflake Data Cloud without the need for third-party connectors or integrations.