Well it seems we are all different in our reactions.
My son had a cold and couldnt vape, as he kept coughing...lol, now me, well I can and do vape with a cold.
However, saying that, I use a mixture of PG and VG. PG as boxhead says is used for germ control, and VG is used in cough syrups, so in theory, the PG should help our immunity and the VG should assist a cure should we get a cold.
Initially vaping can give cold like symptoms, without any virus or bacteria being a contributing factor.
Some people also use Menthol juices when suffering from colds, again, this is bound to help.
Hope thats of use to you