No doubt! You can get dry ice at the stores for about $5- enough for 1 small shipping the boxes cost another $5-$10. Would be pretty costly. Just depends on what the customer wants.
The cost to ship dry ice will be more than standard shipping. Most times dry ice would diminish fast. That is why almost all dry ice shipments are next day or 2 day air.
The cost of that is far more than standard shipping.
Right from UPS:
"The effectiveness of dry ice and gel packs vary, with three days considered the maximum time a product can be stored.
So UPS Next Day Air®, guaranteeing delivery by the next business day, is your best option. If using 2nd Day Air®, remember to add more dry ice or gel freezer packs. Send shipments early in the week."
if this were the case most online shops would not charge an arm and a leg for dry ice shipments on cake, cheesecakes, ice cream etc...
https://www.goldbely.com/cheesecakes
check out how much shipping is on some of these cheesecakes for dry ice.