Not to mention the fact that it's very inconsiderate to bring your illness into the tattoo/piercing studio and risk passing the germs onto others, particularly your artist. They would much rather you cancel and reschedule your appointment than give them an illness that could make them lose income by not being able to go to work.
How far out should you reschedule your appointment? Is a week enough time to get over a cold? Once you start feeling better, that doesn't mean your immune system is up and running at full efficiency. While sick we usually don't get sufficient rest, don't take in proper nourishment, and exhaust our bodies with excessive sneezing, coughing, vomiting, etc. It takes a while for our bodies and immune systems to get back to normal after a period of illness. The first step toward a healthy body is proper nourishment, so start/keep taking your vitamins but also eat a balanced diet. Lack of sufficient calories and/or too much sugar weakens the immune system all by itself. Also, get moving. If you can't walk a mile without being winded, your body isn't up to par. Eating well, drinking plenty of water and being able to walk a mile with ease are good signs that your body is healthy and able to withstand a blow to the immune system. Sometimes this can take a while, even after "just a cold," so when rescheduling your appointment, give yourself at least two or three weeks. It's worth the wait and your body will thank you.