According to CAESAR II Application guide and Technical Reference manual, When snubber is modeled with OPE movement.
In my idea, that means the OPE movement is allowed at OCC case.
But if we inputted stiffness data of snubber, don`t we need to consider OPE movement?

Normally, In case that OPE movement is not considered for modeling a Snubber, Snubber fully restrain piping at OCC case.
but if the stiffness is considered with less than 10^12, a little movement is allowed at OCC case.

I think that is a wrong procedure.

I think you misunderstood the behavior of the snubber. The snubbers allow the thermal displacements under the thermal loads at snubber support locations. There is a friction effect within the snubber but it can be ignored for the thermal calculations.

The snubber in its axial direction will lock the pipe at its position similar to a strut support under the seismic impact forces. There is a small gap in the snubber before it gets into action, but this can be ignored for most of the cases.

Since the sustain and wind loadings are assumed to be permanent push, the snubber will not lock the piping under the these load conditions.

So you need to organize your load cases by considering the behavior of the snubber.

If I were you I would separate the seismic case alone to see what snubber actions you will get. Since you have the operating cases which may include the wind loads you will have the snubber thermal displacement, and you can figure out the displacement range of snubber from the operating cases, and the maximum force from the seismic cases to select.

Please do not replace snubber with a strut, otherwise the thermal loads will act on this support, and the loads will be enormous.

Right, I suggest to read the definition of snubber again.