If you freeze the skin tag off then no it's not painful at all. Once you freeze the skin tag off it will fall off on it's own within a few days and you should have no pain.
You can also cut it off after you tie off the blood to the skin tag but that might be painful.
There's another non painful option of removing skin tags as well. It's called the Tag Band Skin Tag Removal Tool.
You can but it online for around $20.00 and it's a very easy and effective method of removing skin tags without pain.