Analogies can only be pushed so far before they become untrue, because the two things are alike but not the same. For those in the southern hemisphere, like Australia, southern Africa, or Argentina, it is fall, and autumn's march toward winter has begun. Autumn makes for an analogy that is well-suited to the introspection and awareness of death found in Lent and Holy Week. There's also an untruth in the very nature of the spring analogy. You live, you die, you live again.
Christians believe that death is real, and that it's hell to have to go through it even once.
The 'natural' thing is that death is final. Your body's atoms get recycled, but that which made you 'you' is ended. Worse, what you learn during Lent is that this is just and right and necessary. The reason you're not immortal is that you're not good enough or whole enough to be immortal. If not for death, there would be no end to the wrongs you have done or the lies you have lived.