ADF-Execute SSIS that uses ODBC connection

We are planning to migrate our SSIS packages to ADF. We would like to keep all transformations as-is in the packages just switch the data source from on-prem SQL Server to Snowflake (destination stays the same - another on-prem SQL Server). We are using Snowflake ODBC driver. I could set ConnectByroxy property for the destination SQL Server but couldn't find any ConnectByProxy for Snowflake ODBC data source. The package works perfectly alright locally. So I deployed it to ADF (self-hosted IR and Azure-SSIS are all set up and configured).  

I am getting this error -

Error: ADO NET Source has failed to acquire the connection with the following error message: \"ERROR [IM002] [Microsoft][ODBC Driver Manager] Data source name not found and no default driver specified

I installed Snowflake ODBC driver on Self-hosted IR and added a system DSN that matches my local setup. Do I need to do anything else? Wondering if ODBC connection in SSIS package works at all or is this specific to Snowflake ODBC driver?