How does a unit being out of supply effect it? Does the "ice road" allow supply at a full rate or reduced rate?
Unit out of supply is affected in many ways - reduced firepower, morale, increased fatigue, equipment failure rates and many others.
There is some certain supply modifier when supplied through the frozen water hex. However Ladoga is treated as separate sea zone to allow supplies to be traced between ports when it's not frozen as well, and these depend on the shipping capacity being accumulated.