No. Tanning beds are neither a safe nor useful strategy for managing seasonal depression and winter colds.
Certain people with seasonal depression (known as seasonal affective disorder, or SAD) get symptom improvement with light therapy. However, the light boxes designed to treat depression have been engineered to emphasize bright light. But they shield out unnecessary ultraviolet rays. For depression treatment, the eyes must be exposed to the light source. You shouldnt stare directly into the light, but your eyes need to be uncovered.
Tanning beds are another story. They are designed to expose the skin to ultraviolet (UVA) light rays. These are the invisible rays that affect skin pigment and create a tanning effect. Tanning beds minimize brightness.
Many people wrongly believe that newer tanning beds are safe for the skin. Yes, the tanning beds that are used today have been designed to limit UVB rays, so they are less likely to cause sunburns. But they are still associated with a higher risk for melanoma, the life-threatening skin cancer.
Tanning beds can also cause damage to the eyes retina. Since you must wear eye protection in any tanning bed, it is unlikely that this type of light source would have a benefit for seasonal depression.
Tanning beds would not be expected to help protect against colds. Perhaps just the opposite. UVA rays have been shown to cause mild suppression of the immune system.
You should avoid tanning beds to minimize cancer risk. For more information about the dangers of tanning booths, check out this fact sheet