There is unclear evidence stating that Ginger would treat symptoms of common cold, but there is little evidence to suggest that Ginger juice may have antihistaminergic and anticholinergic effects that may help during common cold.
Most of what is know about Ginger is its anti-emetic effects and also lipid lowering effects. However, it is widely used agent during common cold as recommended by many alternative medicine modalities. There is no direct evidence to suggest that Ginger treat symptoms of common cold but there is a study done in China  Ginger juice may exhibits anticholinergic and anti-hisminergic effects through substance P. It is this effect that potentially may help in common cold.
Also, drinking wamr ginger tea may offer help with common cold but it is also due to the fact the warm fluid in itself is helpful in common cold.
- Qian DS, Liu ZS. Pharmacologic studies of antimotion sickness actions of ginger. Zhongguo Zhong Xi Yi Jie He Za Zhi. 1992 Feb;12(2):95-8, 70. Chinese.