Do dried spices offer as many nutrients as fresh spices?
Fresh ginger (sheng jiang) is used to balance formulas, prevent colds through promoting sweat and aid digestion. Dry ginger (gan jiang) also helps digestion if it is caused by a "cold natured" condition. If the stomach or lungs are hot, dry ginger is contraindicated.
Dry ginger also warms the body = The two are completely different. We do not refrigerate fresh ginger, but keep it wrapped in dry paper. It does not dry out too fast but be careful of mold. For other herbs, we do use the dried versions of turmeric (jiang huang), goji berries (gou qi zi) and cinnamon (gui zhi, rou gui). I think nutrient wise, if the spices are from a reputable source, the nutrient value would be suitable for dietary needs.
Most cultures dry their cooking spices/herbs. In my practice of TCM and Taoist cooking, we never talk nutrients ... we only talk qi quality (properties) of food. I think if you could get a wooden box and some good dry paper (parchment) you could keep your spices fresh and nutritious. In good health, be well and travel safe!
Dried spices are great too - they are more concentrated so you'd use a bit less than if it were fresh. Usually it is a tsp dry = 1 Tbsp fresh; however some do not fit the rule like turmeric - so experimenting is key.