Yes, it's best to clean the snow chains before storing them. There are several benefits to doing this:
Extending service life: Cleaning the chain can remove dust, mud, and other impurities from the surface of the chain, preventing them from rusting or corroding the chain during storage. This helps to extend the service life of anti-skid chains.
Maintain chain quality: If there is mud or other dirt on the surface of the chain, it may cause the chain to rust or deteriorate during storage. By cleaning the chain, the quality and performance of the chain can be maintained.
Preparing for next use: Cleaning the chain can ensure that it is in good condition during the next use. If the chain has been cleaned during storage, it can be installed directly on the next use without worrying about dirt or corrosion affecting its effectiveness.

Cleaning snow chains typically involves the following steps:
Rinse the chain with clean water to remove most of the dirt and mud.
Use a soft brush or brush to gently scrub the surface of the chain, ensuring that all impurities are removed.
Wipe the surface of the chain with a dry cloth or tissue to ensure complete dryness.
Before storage, apply a layer of rust inhibitor or lubricating oil to the surface of the chain to further protect it.
By following these simple steps, it is possible to ensure that the snow chains remain in good condition during storage for future use.