I am trying to understand your question. Are you going to thaw your snow sample first?

It seems to me that lyophilization will kill any microorganisms in the snow, except perhaps certain spores. Can you melt the snow and collect the organisms within by vacuum filtration? Then you could just ship the filter.

I want to freeze dry the snow samples @Omar Gonzalez. Either the frozen sample or thawed sample.

Thank you @Adam B Shapiro for the input. I'm concerned to preserve the Ciliates and the bacteria through this process. If it is not much feasible then how the filter be transported in suitable media for re-culturing and other molecular processes?

Or is there any addition of media through its addition can successfully preserve the desired microorganisms by lyophilization?

If freeze-drying is the process you want to perform, I will thaw the sample, add some cryoprotectant (sucrose, trehalose, etc.) and run the freeze drying process. 

I have no experience with this problem, but I will make a suggestion: After collecting the organisms, gently, on a 0.2 micron filter (preferably using the type of vacuum filtration device that has a removable filter), wash the filter off into a 50-ml screw-cap tube with whatever growth medium you think the organisms will enjoy. Make sure the medium almost completely fills the tube, screw the cap on tightly. Transport the tube to the laboratory as quickly as possible on wet ice.

Thank you Omar Gonzalez and @Adam B Shapiro for valuable inputs.

Both processes seems fine to me, but the shipment will take 3-4 days so adding some cryoprotectant will ensure the safe delivery.  

@Omar Gonzalez can you please further give some details in which quantity it should be added? and in what concentration?

I've 30-40ml melt snow samples.