When adding a link to a tile map service in ArcGIS Online you need to reference the service url https://servername/arcgis/rest/services/SnowMap2/mapserver. I would suggest verifying that the server has https enabled if the organizations is https only. It is not possible to reference a local file location.
If the server is on a local server, keep in mind that you won't be able to view the local service outside of your network.
This documentation outlines supported layer types in Map viewer that can be added from a web server: Add layers to maps—ArcGIS Online Help | ArcGIS
This outlines how to add layer items as files. If adding as a file, you would need to first upload the file and then publish it as a supported web layer:
Add layers to maps—ArcGIS Online Help | ArcGIS
I'm not familiar with the format that you referenced in your question, so you may want to verify that the data is provided in a supported format.
-Kelly