Under The Sad Rain:
He's alive. Look at the posters
Just because he appears, in the end, doesn't mean he is alive.. she can be imagining him accompanying her since it was the first snow of the year which they had spent together last time they met.
The time travel here had two trigger points:
1) Accident - Meaning he was not able to fulfil his wish... means dead.
2) When they confess the love - Meaning no regrets anymore.
If he was alive... there was no need for time travel .. since he can still confess his love.. there is only lost years... he could still fulfill his wish