There is a pass - Alpine-Takayama-Matsumoto Area Tourist Pass that covers Nagoya to and fro alpine route, and within alpine route as well. Only JR pass can support the route from Osaka to and fro Nagoya. Otherwise, it costs 6000+yen for Shinkansen.
If you want to cover the route from Osaka on a day-trip, then don't get that pass because it does not support Shinkansen. You definitely need Shinkansen for a day trip.
What I did was to stay at Toyama for a night, then take the earliest train to Alpine route. If you are only there for the snow wall, a day trip from Osaka should be no problem. If you want to cover the full route, including the Kurobe dam, then it's not quite possible IMO.