Lots of good answers here already. The tagging for a backcountry ski piste does not conflict with the tagging for a hiking trail so you can put both tags on the same way.
With regard to path vs footway, that convention seems to vary depending on where you are in the world. But as a person who renders maps for hiking, please put at least a surface on the way. Paved/unpaved at the minimum. Trail visibility and SAC scale are also very helpful. The issue is that since trail tagging does not have a single agreed highway=* value the renderers have to look at those secondary tags to determine if this is a smooth walkway suitable for pushing a baby stroller or a way that requires good footwear and maybe hiking poles, etc. I wrote up the difficulties I ran into trying to figure out how to identify hiking trails in OSM about 5 years ago and the situation has not changed much.