Shoes for slow and steady with a load. Less skill required than skis and they are pretty straightforward for hill climbing.
Takes a LOT more effort than walking to go very far.

Skis for much faster travel but with more chances of crashing and injury (even on the flats). And getting uphill requires skins or wax changes. Getting downhill without crashing a lot requires considerable training/practice. The one injury I've seen a buddy have was ACL rupture while we were XC skiing because of beginner technique (neither of us was any good).

Frankly, unless I was in the mountains, I'd just wait for the snow to melt down a ways so I could walk on it if I had to travel a long ways by manual means.